GMAT Practice Question: 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?
- 7
- 8
- 9
- 10
- 11
Topics: word problems, linear equations, translations
Solution
Step 1
We create variables to represent the number of juniors and number of seniors.
j = \text{number of juniors}, \quad s = \text{number of seniors}
Step 2
We translate the phrase \textbf{\text{"17 juniors and seniors"}} into an equation representing their total count.
j + s = 17
Step 3
We translate the phrases \textbf{\text{"each junior has written 2 book reports and each senior has written 3 book reports"}} and \textbf{\text{"total of 44 book reports"}} into an equation.
2j + 3s = 44
Step 4
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
Answer
There are 7 juniors in the class.
