AnswersGA-8th Grade MathematicsModeling Real-World Multistep Equations

Modeling Real-World Multistep Equations Answers

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1
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Aviva is comparing her age to her sisters’ ages. Kanti is 3 years younger. Aviva’s older sister, Lakshmi is twice as old as Kanti. Which expression correctly completes the table?Sister’s AgesSisterAgeAvivaxKantix – 3Lakshmi?

A
2 x minus 3
Option A
B
2 (x minus 3)
Option B
C
2x
D
(x minus 3) + 2
Option D
2
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A rectangle has a width of x and a length that is 13 less than twice its width. Which rectangle shows the same relationship?

A
A rectangle with a length of 2 x minus 13 and width of x.
Option A
B
A rectangle with a length of 2 (x minus 13) and width of x.
Option B
C
A rectangle with a length of x + 2 and width of x minus 13.
Option C
D
A rectangle with a length of 13 minus 2 x and width of x.
Option D
3

Danessa is working with consecutive even numbers. If x is her first number, which expression represents her second number?

A
x + 1
B
x – 1
C
x + 2
D
2x
4

Roderick is counting the change on his dresser. He has twice as many pennies as he does dimes. He has twice the amount of dimes as he does nickels. He has 3 fewer quarters than dimes. Which variable definition would be easiest for Roderick to use when writing expressions for the number of all the coins?

A
x = number of pennies because the penny has the least value of all the coins.
B
x = number of nickels because there are fewer nickels than any other coin.
C
x = number of dimes because all the other coins are compared to dimes.
D
x = number of quarters because it has the greatest value of all the coins.
5

Jolianne worked half as many hours as Andrew. Jolianne makes $10 per hour and has saved $27. Andrew makes $8 per hour and has no money saved. After getting paid, they have the same amount of money. Andrew’s Table for Comparing MoneyNameRate of pay(per hour)Hours workedJolianne10Andrew8tAndrew’s equation: Jolianne’s Table for Comparing MoneyNameRate of pay(per hour)Hours workedJolianne10tAndrew82t Jolianne’s equation: Andrew claims that only his table and equation are correct, but Jolianne claims that both tables and equations are valid. Which statement regarding their claims is true?

Question illustration
A
Andrew is correct because t cannot be used to represent the number of hours Jolianne worked.
B
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did.
C
Jolianne is correct because if one lets t = hours Andrew worked, then his equation is valid. If one lets t = hours Jolianne worked, then Andrew worked twice as many so her equation is valid, too.
D
Jolianne is correct because when solving t in her equation, t = hours Jolianne worked, and when solving for t in Andrew’s equation, t = hours Jolianne worked so they are equal.
6

Elliott is counting the change from a class fundraiser. He has half as many quarters as nickels, and he has 7 fewer dimes than nickels. The total value of coins is $5.90. He wrote the equation . Which statements identify Elliott’s errors? Select the two correct answers.

Question illustration
A
He should have written the expression for the number of dimes as x – 7.
B
He should have written the coin values as 5, 10, and 25 and not as 0.5, 0.10, and 0.25.
C
He should have written the coin value for the nickel as 0.05.
D
He should have translated the scenario as value of all dimes = value of all nickels and value of all quarters = value of all nickels.
E
He should have written the expression for number of nickels as 2x.

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