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COMALGE PRACTICE EXERCISE 3

I. Find the solution set of each equation. Check if necessary

A. 1. 4)2x)(1x3( 5. 010x7 2 =2. 3)1x)(1x2( = 6.

1x

1

3x

4

2x

2 +3. 10)1x( 2 = 7.

2x

3x2

x2

3x

4x

112 +=++

4. 049x16 2 = 8. 21x

1

2x

1 =B. 1. 09x8x 24 = 14. 0

3x

1x45

1x

3x = +++ +

+2. 036x13x 24 = 15. 1x21x3 3. 09x32x16 24 = 16. 2w6w5 =4. 09x77x36 24 = 17. 5x411x3 +5. 01x13x36 3

23

4

= 18. t212t3 6. 01z3z3 2

1

1 =

19. 47x2x56 +7. 03)x2x(2)x2x( 222 = 20. 19x512x3 =8. 032)x4x(4)x4x( 222 = 21. 43x11x5 =9. 02)x3x2()x3x2( 222 = 22. 9x54x31x +

10. 011x

3x

1x

3x2

2 =++

+ 23. 01x83x21x =11. 01)

1x2

3x(4

1x2

3x3

2 =+

+ 24. 53x42x8 =12. 32)

1x

x(4

1x

x2 =

25. 41x53 =

13. 03x2

4x67

4x

3x2 = + 26. 28x2x4 2 =

II. Solve the following problems.

1. Find a number such that 10 less than two-thirds the number is one-fourth the number.

2. The smaller of two numbers is 9 less than the larger and their sum is 37. Find the numbers.

3. The sum of a number and its reciprocal is15

34. Find the number.

4. If the larger of two integers, whose sum is 88, is divided by the smaller, the quotient is 5

and the remainder is 10. What are the two numbers ?

5. The sum of the reciprocals of two consecutive even integers is60

11. What are the integers ?

6. Find 2 consecutive odd integers so that the square of the larger exceeds their product by 34.( Ans. 15 & 17 )

7. Find two consecutive positive integers such that the sum of their squares is 113.

8. Find two consecutive odd integers whose product exceeds three times their sum by 15.

COMALGE PRACTICE EXERCISE 3

9. The tens digit of a number is 3 less than the units digit. If the number is divided by the sum

of the digits, the quotient is 4 and the remainder is 3. What is the original number ?

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10. The tens digit is 5 more than the unit digit. If the sum of their squares is 53, find the number.

11. Dianne invests P3500, part at 3%, part at 4%. How much does she invest at each rate if she

receive in one year interest of P115? ( P2500 at 3% ; P1000 at 4% )

12. Sonia invests some of his money at 5% and twice as much at 5 %. If his total income is $125,

find the amount invested at each rate. ( $781.25 at 5% ; $1562.50 at 5 % )

13. Judy wants to invest $ 50,000. Part of it is invested in a fund that pays 12.5% and the

remainder in one that pays 14%. Find the amount invested at each rate if the annual income

from the two is $ 6640.

14. An invested wishes to realize a return of 12% from a total of two investments. If he has

P 10,000 invested at 10%, how much additional money should be invested at 16%?Ans. P 5,000

III. Determine whether the system is consistent and independent, consistent and dependent or

inconsistent.

1. 2x + 4y = 8 3. x + 2y = 5 5. 3x + 2y = 6 7. 2x + 3y = 5

x + 2y = 4 3x -15 = -6y 6x + 4y = 12 -6x - 9y = -10

2. 5x + 2y = 7 4. 3x + 2y = 3 6. x + y = 6 8. 4x + 2y = -83x + 5y = 8 4y x = -7 3x + 3y = -10 x 2y = 7

IV. Solve each linear system by (a) addition or subtraction (b) by substitution (c) by graphing

1. 2x + y = 2 3. x + 2y = 5 5. 3x + 2y = 6 7. 2x + 3y = 5

3x y = -7 3x + 2y = 11 6x + 4y = 12 -6x - 9y = -15

2. 5x + 2y = 7 4. 3x + 2y = 3 6. x + y = 6 8. 4x + 2y = -8

3x + 5y = 8 4x y = -7 3x + 3y = -10 x 2y = -7

V. Solve each system of equations by addition or subtraction.

1. 4x 3y = -4 4. 3x + 2y + 2z = -1 6. a + 2b c = -7 8. 17y1

x

3 3x 2y = -4 5x 3y + 4z = -3 2a + 3b + 2c = -3 0y

5x2 =

2x + y + 2z = -2 a 2b 2c = 3

2. 27

41 yx = 5. 3x + 2y 5z = 1 7. 2x + 3y + 4z = 4

1yx41

21 = -13 y 24z = 11 2x 8z = -1

x + 5y + 8z = - 5 4x 6y +4z = -1

3.

3

4

3

z3

y2

x1

z1

y1

x2

z1y2x3

===

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