algebra with whole numbers
DESCRIPTION
Algebra with Whole Numbers. Write equations and Solve. I think of a number, multiply it by 2 and then add 8. The answer is 50. Find the number. Write down the equation and solve it for n. I think of a number, multiply it by 3 and then subtract 9. The answer is 60. Find the number. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/1.jpg)
Algebra with Whole Numbers
Write equations and Solve
![Page 2: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/2.jpg)
Write down the equation and solve it for n
• I think of a number, multiply it by 2 and then add 8. The answer is 50. Find the number.
![Page 3: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/3.jpg)
Write down the equation and solve it for n
• I think of a number, multiply it by 3 and then subtract 9. The answer is 60. Find the number.
![Page 4: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/4.jpg)
Write down the equation and solve it for n
• I think of a number, divide it by 2 and then add 6. The answer is 30. Find the number.
![Page 5: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/5.jpg)
Write down the equation and solve it for n
• I think of a number, divide it by 3 and then subtract 5. The answer is 20. Find the number.
![Page 6: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/6.jpg)
Write down the equation and solve it for x
• John is 5 years older than Mary. Their ages total 33 years. Find their ages.
• (Let Mary’s age be x years.)
![Page 7: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/7.jpg)
Write down the equation and solve it for x
• John is 5 years older than Mary. Their ages total 33 years. Find their ages.
• (Let Mary’s age be x years.)
![Page 8: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/8.jpg)
Write down the equation and solve it for x
• John is 5 years older than Mary. Their ages total 33 years. Find their ages.
• (Let Mary’s age be x years.)
![Page 9: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/9.jpg)
Write down the equation and solve it for x
• John is 5 years older than Mary. Their ages total 33 years. Find their ages.
• (Let Mary’s age be x years.)
Mary is 14 and John is 19.
![Page 10: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/10.jpg)
Write down the equation and solve it for x
• James is 8 years younger than Margaret. Their ages total 42 years. Find their ages.
• (Let Margaret's age be x years.)
![Page 11: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/11.jpg)
Write down the equation and solve it for x
• James is 8 years younger than Margaret. Their ages total 42 years. Find their ages.
• (Let Margaret's age be x years.)
![Page 12: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/12.jpg)
Write down the equation and solve it for x
• James is 8 years younger than Margaret. Their ages total 42 years. Find their ages.
• (Let Margaret's age be x years.)
![Page 13: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/13.jpg)
Write down the equation and solve it for x
• James is 8 years younger than Margaret. Their ages total 42 years. Find their ages.
• (Let Margaret's age be x years.)
Margaret is 25 and James is 17.
![Page 14: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/14.jpg)
Write down the equation and solve it for x
• Dad is twice as old as Dave and together their ages total 63 years. Find their ages.
• (Let Dave's age be x years.)
![Page 15: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/15.jpg)
Write down the equation and solve it for x
• Dad is twice as old as Dave and together their ages total 63 years. Find their ages.
• (Let Dave's age be x years.)
![Page 16: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/16.jpg)
Write down the equation and solve it for x
• Dad is twice as old as Dave and together their ages total 63 years. Find their ages.
• (Let Dave's age be x years.)
![Page 17: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/17.jpg)
Write down the equation and solve it for x
• Dad is twice as old as Dave and together their ages total 63 years. Find their ages.
• (Let Dave's age be x years.)
Dave is 21 and his dad is 42.
![Page 18: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/18.jpg)
Write down the equation and solve it for x
• Steptoe is 3 times the age of his son and 46 years older than his son. Find their ages. (Let the son's age be x years).
![Page 19: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/19.jpg)
Write down the equation and solve it for x
• Steptoe is 3 times the age of his son and 46 years older than his son. Find their ages. (Let the son's age be x years).
![Page 20: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/20.jpg)
Write down the equation and solve it for x
• Steptoe is 3 times the age of his son and 46 years older than his son. Find their ages. (Let the son's age be x years).
![Page 21: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/21.jpg)
Write down the equation and solve it for x
• Steptoe is 3 times the age of his son and 46 years older than his son. Find their ages. (Let the son's age be x years).
The son is 23 and Steptoe is 69.
![Page 22: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/22.jpg)
Write down the equation and solve it for x
• Peter and Paul together earn a total of $500 every week. Of this Peter earns $40 more than Paul. Find how much each one earns per week.
• (Let Paul earn $x).
Paul earns is $230 and Peter earns $270.
![Page 23: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/23.jpg)
Write down the equation and solve it for x
• Mary and Jane together earn a total of $600 every week. Of this Mary earns $80 less than Jane. Find how much each one earns per week.
• (Let Jane earn $x).
![Page 24: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/24.jpg)
Write down the equation and solve it for x
• Mary and Jane together earn a total of $600 every week. Of this Mary earns $80 less than Jane. Find how much each one earns per week.
• (Let Jane earn $x).
![Page 25: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/25.jpg)
Write down the equation and solve it for x
• Mary and Jane together earn a total of $600 every week. Of this Mary earns $80 less than Jane. Find how much each one earns per week.
• (Let Jane earn $x).
![Page 26: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/26.jpg)
Write down the equation and solve it for x
• Mary and Jane together earn a total of $600 every week. Of this Mary earns $80 less than Jane. Find how much each one earns per week.
• (Let Jane earn $x).
Jane earns is $340 and Mary earns $260.
![Page 27: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/27.jpg)
Write down the equation and solve it for x
• Michael earns 3 times as much as Geoffrey and together their wages total $84 000 for the year. Find how much each one earns per annum.
• (Let Geoffrey earn $x).
![Page 28: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/28.jpg)
Write down the equation and solve it for x
• Michael earns 3 times as much as Geoffrey and together their wages total $84 000 for the year. Find how much each one earns per annum.
• (Let Geoffrey earn $x).
![Page 29: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/29.jpg)
Write down the equation and solve it for x
• Michael earns 3 times as much as Geoffrey and together their wages total $84 000 for the year. Find how much each one earns per annum.
• (Let Geoffrey earn $x).
Geoffrey earns is $21000 and Michael earns $63000.
![Page 30: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/30.jpg)
Write down the equation and solve it for x
• May earns 4 times as much as June and this amounts to a difference in their wages of $60 000 for the year. Find how much each one earns per annum.
• (Let June earn $x).
![Page 31: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/31.jpg)
Write down the equation and solve it for x
• May earns 4 times as much as June and this amounts to a difference in their wages of $60 000 for the year. Find how much each one earns per annum.
• (Let June earn $x).
![Page 32: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/32.jpg)
Write down the equation and solve it for x
• May earns 4 times as much as June and this amounts to a difference in their wages of $60 000 for the year. Find how much each one earns per annum.
• (Let June earn $x).
June earns is $20000 and May earns $80000.
![Page 33: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/33.jpg)
Write down the equation and solve it for x
• Tom is twice as old as Dick. Harriot is 3 times as old as Dick. Altogether their ages total 120 years. Find their ages.
• (Let Dick's age be x years).
![Page 34: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/34.jpg)
Write down the equation and solve it for x
• Tom is twice as old as Dick. Harriot is 3 times as old as Dick. Altogether their ages total 120 years. Find their ages.
• (Let Dick's age be x years).
![Page 35: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/35.jpg)
Write down the equation and solve it for x
• Tom is twice as old as Dick. Harriot is 3 times as old as Dick. Altogether their ages total 120 years. Find their ages.
• (Let Dick's age be x years).
Dick is 20, Tom is 40 and Harriot is 60.
![Page 36: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/36.jpg)
Write down the equation and solve it for x
• Peter is 7 years older than Paul. Mary is 3 years younger than Paul. Altogether their ages total 64 years. Find their ages.
• (Let Paul's age be x years).
![Page 37: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/37.jpg)
Write down the equation and solve it for x
• Peter is 7 years older than Paul. Mary is 3 years younger than Paul. Altogether their ages total 64 years. Find their ages.
• (Let Paul's age be x years).
![Page 38: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/38.jpg)
Write down the equation and solve it for x
• Peter is 7 years older than Paul. Mary is 3 years younger than Paul. Altogether their ages total 64 years. Find their ages.
• (Let Paul's age be x years).
Paul is 20, Peter is 27 and Mary is 17.
![Page 39: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/39.jpg)
Write down the equation and solve it for x
• Dad is twice as old as his son. His daughter is 5 years younger than his son. Altogether their ages total 95 years. Find their ages.
• (Let the son's age be x years).
![Page 40: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/40.jpg)
Write down the equation and solve it for x
• Dad is twice as old as his son. His daughter is 5 years younger than his son. Altogether their ages total 95 years. Find their ages.
• (Let the son's age be x years).
![Page 41: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/41.jpg)
Write down the equation and solve it for x
• Dad is twice as old as his son. His daughter is 5 years younger than his son. Altogether their ages total 95 years. Find their ages.
• (Let the son's age be x years).
The son is 25. Dad is 50 and the daughter is 20.
![Page 42: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/42.jpg)
Write down the equation and solve it for x
• Grandma is 3 times as old as Mum. Dad is 6 years older than Mum. Altogether their ages total 156 years. Find their ages.
• (Let the Mum's age be x years).
![Page 43: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/43.jpg)
Write down the equation and solve it for x
• Grandma is 3 times as old as Mum. Dad is 6 years older than Mum. Altogether their ages total 156 years. Find their ages.
• (Let the Mum's age be x years).
![Page 44: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/44.jpg)
Write down the equation and solve it for x
• Grandma is 3 times as old as Mum. Dad is 6 years older than Mum. Altogether their ages total 156 years. Find their ages.
• (Let the Mum's age be x years).
Mum is 30. Grandma is 90 and Dad is 36.
![Page 45: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/45.jpg)
Write down the equation and solve it for x
• Two angles are supplementary if they add up to . Find the 2 supplementary angles which are such that one is more than the other.
• (Let the smaller of the 2 angles be ).
![Page 46: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/46.jpg)
Write down the equation and solve it for x
• Two angles are supplementary if they add up to . Find the 2 supplementary angles which are such that one is more than the other.
• (Let the smaller of the 2 angles be ).
![Page 47: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/47.jpg)
Write down the equation and solve it for x
• Two angles are supplementary if they add up to . Find the 2 supplementary angles which are such that one is more than the other.
• (Let the smaller of the 2 angles be ).
One angle is 450 and the other is 1350.
![Page 48: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/48.jpg)
Write down the equation and solve it for x
• Two angles are complementary if they add up to 900. Find the 2 complementary angles which are such that one is 5 times the other. (Let the smaller of the 2 angles be x).
![Page 49: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/49.jpg)
Write down the equation and solve it for x
• Two angles are complementary if they add up to 900. Find the 2 complementary angles which are such that one is 5 times the other. (Let the smaller of the 2 angles be x).
![Page 50: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/50.jpg)
Write down the equation and solve it for x
• Two angles are complementary if they add up to 900. Find the 2 complementary angles which are such that one is 5 times the other. (Let the smaller of the 2 angles be x).
One angle is 150 and the other is 750.
![Page 51: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/51.jpg)
Write down the equation and solve it for x
• The angles of a triangle add up to 1800. Find the size of the angles in triangle ABC if angle B is 200 less than angle A and angle C is 3 times angle A.
• (Let the size of angle A be).
![Page 52: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/52.jpg)
Write down the equation and solve it for x
• The angles of a triangle add up to 1800. Find the size of the angles in triangle ABC if angle B is 200 less than angle A and angle C is 3 times angle A.
• (Let the size of angle A be).
![Page 53: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/53.jpg)
Write down the equation and solve it for x
• The angles of a triangle add up to 1800. Find the size of the angles in triangle ABC if angle B is 200 less than angle A and angle C is 3 times angle A.
• (Let the size of angle A be).
A = 400, B = 200 and C = 1200.
![Page 54: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/54.jpg)
Write down the equation and solve it for x
• The angles of a quadrilateral add up to 3600. Find the size of the angles in quadrilateral ABCD if angle B is 300 less than angle A, angle C is 400 more than angle A and angle D is twice angle A. (Let the size of angle A be x).
![Page 55: Algebra with Whole Numbers](https://reader031.vdocuments.site/reader031/viewer/2022013112/56813455550346895d9b3baf/html5/thumbnails/55.jpg)
Write down the equation and solve it for x
• The angles of a quadrilateral add up to 3600. Find the size of the angles in quadrilateral ABCD if angle B is 300 less than angle A, angle C is 400 more than angle A and angle D is twice angle A. (Let the size of angle A be x).
A = 700, B = 400, C = 1100 and D=140.
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Exercise 13
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1. The distance, d km, that an athlete walks is given by the formula where t is the time
for which she walks in hours.
• Find the distance she walks in 3 hours.
• Find the time it takes her to walk the length of a marathon (i.e. 42 km).
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2. The distance, d km, that an athlete jogs is given by the formula where t is the time
for which he jogs in minutes.
• Find the distance that he jogs in 1 hour (i.e. 60 minutes).
• Find the time (in hours and minutes) for him to jog the length of a half marathon (i.e. 21 km).
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3. The money saved by a youth since her 12th birthday, $S, is given by the formula where n is the
number of weeks which have elapsed since her 12th birthday.
Find how much she saved
• by her next birthday (i.e. 52 weeks after her 12th birthday).
• initially (i.e. on her 12th birthday).
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3. The money saved by a youth since her 12th birthday, $S, is given by the formula where n is the
number of weeks which have elapsed since her 12th birthday.
• Find how many weeks after her 12th birthday she will have saved $1000
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4. The temperature, t, of water in a kettle is given by the formula where n is the number of seconds after
the kettle was turned on. Find the temperature of the
water in the kettle
• 200 seconds after it was turned on
• 2 minutes (i.e. 120 seconds) after it was turned on
• initially (i.e. at the instant that the kettle was turned on).
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4. The temperature, t, of water in a kettle is given by the formula where n is the number of seconds after
the kettle was turned on. Find (in minutes and
seconds) how long it takes for the water in the kettle
• to reach body temperature (i.e. 370 C.)
• to boil (i.e. to reach 1000 C.)
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4. The temperature, t, of water in a kettle is given by the formula where n is the number of seconds after
the kettle was turned on. Find (in minutes and
seconds) how long it takes for the water in the kettle
• to reach body temperature (i.e. 370 C.)
• to boil (i.e. to reach 1000 C.)