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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?

Explanation	Calculations	Help
$We create variables to represent the number of juniors and number of seniors.$	$j = number of juniors, s = number of seniors$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the phrase "17 juniors and seniors" into an equation representing their total count.$	$j + s = 17$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We translate the phrases "each junior has written 2 book reports and each senior has written 3 book reports" and "total of 44 book reports" into an equation.$	$2 j + 3 s = 44$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute s = 17 - j into the second equation and use algebra to solve for j .$	$s = 17 - j 2 j + 3 (17 - j) = 44 2 j + 51 - 3 j = 44 - j + 51 = 44 - j = - 7 j = 7$	Theory & Tactics Method Card EQUA1-A Click to view full details

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There are 7 juniors in the class.

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?

Explanation	Calculations	Help
$We create variables to represent the number of juniors and number of seniors.$	$j = number of juniors, s = number of seniors$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the phrase "17 juniors and seniors" into an equation representing their total count.$	$j + s = 17$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We translate the phrases "each junior has written 2 book reports and each senior has written 3 book reports" and "total of 44 book reports" into an equation.$	$2 j + 3 s = 44$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute s = 17 - j into the second equation and use algebra to solve for j .$	$s = 17 - j 2 j + 3 (17 - j) = 44 2 j + 51 - 3 j = 44 - j + 51 = 44 - j = - 7 j = 7$	Theory & Tactics Method Card EQUA1-A Click to view full details

Scroll horizontally to view all columns

There are 7 juniors in the class.