In a certain history class of 17 juniors and seniors, each junior has written 2 book reports and...

Question

In a certain history class of 17 juniors and seniors, each junior has written 2 book reports and each senior has written 3 book reports. If the 17 students have written a total of 44 book reports, how many juniors are in the class?

GMAT Panda · Accepted Answer

There are 7 juniors in the class. We create variables to represent the number of juniors and number of seniors. j = number of juniors, s = number of seniors We translate the phrase "17 juniors and seniors" into an equation representing their total count. j + s = 17 We translate the phrases "each junior has written 2 book reports and each senior has written 3 book reports" and "total of 44 book reports" into an equation. 2j + 3s = 44 We substitute s = 17 - j into the second equation and use algebra to solve for j. s = 17 - j 2j + 3(17 - j) = 44 2j + 51 - 3j = 44 -j + 51 = 44 -j = -7 j = 7

Explanation	Calculations	Help
$We create variables to represent the number of juniors and number of seniors.$	$j = number of juniors, s = number of seniors$
$We translate the phrase "17 juniors and seniors" into an equation representing their total count.$	$j + s = 17$
$We translate the phrases "each junior has written 2 book reports and each senior has written 3 book reports" and "total of 44 book reports" into an equation.$	$2 j + 3 s = 44$
$We substitute s = 17 - j into the second equation and use algebra to solve for j .$	$s = 17 - j 2 j + 3 (17 - j) = 44 2 j + 51 - 3 j = 44 - j + 51 = 44 - j = - 7 j = 7$

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