Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-There are 14 more sophomores than juniors in an algebra class. If there are 82 students in this class, find the number of sophomores and the number of juniors in the class.
A) 34 sophomores; 48 juniors
B) 96 sophomores; 68 juniors
C) 82 sophomores; 68 juniors
D) 48 sophomores; 34 juniors

Question

Quizplus · Accepted Answer

Let the number of juniors be $j$ and the number of sophomores be $s$. The problem states that there are 14 more sophomores than juniors, so $s = j + 14$. It also states that the total number of students is 82, so $s + j = 82$. Substituting the first equation into the second gives $j + 14 + j = 82$, which simplifies to $2j + 14 = 82$. Solving for $j$ gives $2j = 68$, so $j = 34$. Substituting $j = 34$ back into the equation $s = j + 14$ gives $s = 34 + 14 = 48$. Therefore, there are 48 sophomores and 34 juniors.

Let X Represent the Number