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Practice Problems
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Practice Problems
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Practice Problem #1
• What is the sum of the solutions fory = x + 33x + y = 5
ANSWER
Answer 1)
• What is the sum of the solutions fory = x + 33x + y = 5
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Practice Problem #2
• Solve. Write your answer as an ordered pair.
-0.5x + y = - 1y - 1 = 2 -7x + 2
ANSWER
Answer 2)Step 1: solve each equation for y
-0.5x + y = - 1 becomes y = 0.5x - 1y - 1 = 2 -7x + 2 becomes y = -7x +5
Step 2: solve by substitution0.5x – 1 = -7x + 57.5x = 6x = 0.8
Step 3: use y - 1 = 2 -7x + 2, substitution 0.8 for x y – 1 = 2 – 7(0.8) + 2 y = 2 – 5.6 + 2 + 1
y = -0.6 Answer: (0.8, -0.6)Return to
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Practice Problem #3
• Solve the system. What is the sum of x and y?
• y = 9x + 20• y = -1/3 x + 13
ANSWER
Answer 3)
• y = 9x + 20• y = -1/3 x + 13
Use substitution9x + 20 = -1/3x +
13+1/3x +1/3x9 1/3x + 20 = 13 Return to
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9 1/3x + 20 = 13 -20 -209 1/3x = -79 1/3 9 1/3 x = -3/4y = 9(-3/4) + 20y = 13.25Sum is -0.75 + 13.25Sum is 12.5
Practice Problem #4
• Solve. What is the product of x and y?
• 2y = 3x + 4• y = -2x - 1.5
ANSWER
Answer 4)
• Solve. What is the product of x and y?
• 2y = 3x + 4• y = -2x - 1.5• Answer: -0.5
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Practice Problem #5
• Clair bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item.
ANSWER
Answer 5)
Let x = price per bar of soap, y = price per sponge
3x + 5y = 2.315x + 3y = 3.05
x = $0.52y = $0.15
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Practice Problem #6
• Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast, and $.90 for one egg and one piece of toast. Write and graph a system of equations to determine how much she charges for each egg and each piece of toast. Let x represent the number of eggs and y the number of pieces of toast.
ANSWER
Answer 6)
Let e = price per egg, t = price per slice of toast2e + t = 1.50e + t = 0.90
$0.60 per egg$0.30 for toast
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Practice Problem #7
• Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has.
ANSWER
Answer 7)
Let x = 1 dollar bills, y = 5 dollar bills
x + y = 14x + 5y = 30
4 five-dollar bills10 one-dollar bills
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Practice Problem #8
• Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. There were 240 tickets sold for a total of $1,155.00. Find the number of adult tickets sold and the number of student tickets sold.
ANSWER
Answer 8)
6a + 4.5s = 1155 a + s = 240
50 student and 190 adult tickets
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Practice Problem #9
• Tom has a collection of 27 CDs and Nita has a collection of 18 CDs. Tom is adding 3 CDs a month to his collection while Nita is adding 6 CDs a month to her collection. Write and graph a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
ANSWER
Answer 9)
Tom: y = 27 + 3xNita: y = 18 + 6x
3 months
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Months
Num
ber
of
CD
’s
10
2
0 3
0 4
0 5
0
1 2 3 4 5 6