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At the beginning of the week, Josh had 32 computer games,
133% as many computer games as Peter had. By the end of the week, Josh gave
25% of his computer games to Peter. How many computer games did Josh and Peter each have by the end of the week?
Choose 1 answer:
(A) Josh had 8 games; Peter had 24 games.
(B) Josh had 24 games; Peter had 8 games.
(c) Josh had 24 games; Peter had 32 games.
(D) Josh had 32 games; Peter had 24 games.

At the beginning of the week, Josh had $32$ computer games, $133 \%$ as many computer games as Peter had. By the end of the week, Josh gave $25 \%$ of his computer games to Peter. How many computer games did Josh and Peter each have by the end of the week? $\newline$ Choose $1$ answer: $\newline$ (A) Josh had $8$ games; Peter had $24$ games. $\newline$ (B) Josh had $24$ games; Peter had $8$ games. $\newline$ (C) Josh had $24$ games; Peter had $32$ games. $\newline$ (D) Josh had $32$ games; Peter had $24$ games.

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Quantities that combine to zero: word problems

Full solution

Q. At the beginning of the week, Josh had

32

computer games,

133 \%

as many computer games as Peter had. By the end of the week, Josh gave

25 \%

of his computer games to Peter. How many computer games did Josh and Peter each have by the end of the week?

\newline

Choose

1

answer:

\newline

(A) Josh had

8

games; Peter had

24

games.

\newline

(B) Josh had

24

games; Peter had

8

games.

\newline

(C) Josh had

24

games; Peter had

32

games.

\newline

(D) Josh had

32

games; Peter had

24

games.

Determine Initial Games: Determine the number of computer games Peter had at the beginning of the week. $\newline$ Josh had $133\%$ as many computer games as Peter. Let $x$ be the number of games Peter had. Then, $1.33x = 32$ . $\newline$ Solve for $x$ : $x = \frac{32}{1.33}$ . $\newline$ $x \approx 24.06$ , which we round to $24$ since the number of games must be a whole number.
Calculate Games Given: Calculate the number of games Josh gave to Peter. $\newline$ Josh gave away $25\%$ of his $32$ games, which is $0.25 \times 32 = 8$ games.
Calculate Games Left: Determine the number of games Josh had left after giving games to Peter. $\newline$ Josh had $32$ games and gave away $8$ , so he had $32 - 8 = 24$ games left.
Calculate Final Games: Determine the number of games Peter had after receiving games from Josh. $\newline$ Peter started with $24$ games and received $8$ from Josh, so he had $24 + 8 = 32$ games by the end of the week.

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