1995 AMC 8 Problem 16

Attempt Problem 16 of the 1995 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

16.

Students from three middle schools worked on a summer project. Seven students from Allen School worked for 33 days. Four students from Balboa School worked for 55 days. Five students from Carver School worked for 99 days. The total amount paid for the students’ work was $774.\$774. Assuming each student received the same amount for a day’s work, how much did the students from Balboa School earn altogether?
$9.00\$9.00
$48.38\$48.38
$180.00\$180.00
$193.50\$193.50
$258.00\$258.00
Answer: C
Concepts:rate
Small hint:
Compute the total number of student-days worked across all three schools
Big hint:
Divide $774\$774 by the total student-days to get the pay per student-day
Solution:
The total student-days are 7×3+4×5+5×97 \times 3 + 4 \times 5 + 5 \times 9 =21+20+45= 21 + 20 + 45 =86.= 86.
So each student-day pays $774÷86=$9.\$774 \div 86 = \$9. Balboa worked 2020 student-days, earning 20×$9=$180.20 \times \$9 = \$180.
Thus, the correct answer is C .
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