Question

Steph scored $15$ baskets out of $20$ attempts in the first half of a game, and $10$ baskets out of $10$ attempts in the second half. Candace took $12$ attempts in the first half and $18$ attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?

$7$

$8$

$9$

$10$

$11$

Solution:

Steph made $25$ baskets in $30$ attempts. Candace also took $12+18=30$ attempts, and their overall percentages were the same, so Candace also made $25$ baskets.

Let $f$ be Candace's first-half baskets and $s$ be her second-half baskets. Then $f+s=25$ .

Steph's first-half percentage was $\frac{15}{20}=\frac34$ , so $\frac{f}{12}<\frac34$ , giving f<9. Steph's second-half percentage was $1$ , so s<18.

Thus $f\le8$ and $s\le17$ . Since $f+s=25$ , the only possibility is $f=8$ and $s=17$ , so $s-f=9$ .

Thus, the correct answer is C.

2022 AMC 8 Problem 21

Solution:

Problem 21 in Other Years