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

Practice Problems

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

Practice Problems

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

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