Simple SAT question concerning percents

Question

Here is a simple question I am struggling with:

Allison, Jonathan, and Jennifer are teachers at a school. There classes contain a total of 82 students. Jonathan's class is 25% larger than Jennifer's class. Allison's class has 9 more students than Jennifer's class. How many students are in Allison's class?

A. 35 students B. 26 students C. 31 students D. 14 students E. 25 students

Here is how I tried to solve:

Let Allison's class be x, Jonathan's be y and Jenn's be z.

$x+y+z=82$

$0.75y=z$ (y should be 25% larger than z)

$z=x-9$

And then, I tried to solve it for $x$ but didn't get the right answer. What I seem to be missing is the percent part:

When it says, Jonathan's class is 25% larger than Jennifer's class, does it mean 25% OF Jonathan's class or Jonathan's class is 125% OF Jennifer's?

Answer 1

$y$ being $25\%$ larger than $z$ should be $y=1.25 z$. What you have written is $y=(4/3)z$, which is $y$ being $33\%$ larger than $z$.

When it says, Jonathan's class is 25% larger than Jennifer's class, does it mean 25% OF Jonathan's class or Jonathan's class is 125% OF Jennifer's?

The latter is the correct interpretation.

Answer 2

Remember you can find the percent of something by multiplying that number by the percent written as a decimal. For example, if I wanted to find $20\%$ of 120, I could find $120*0.20$.

Let $x$ be the amount of students in Jennifer's class. Then Jonathan's class must have $x+.25x$ student (the same amount as Jennifer's plus another $25\%$ more). Allison's class must be $x+9$. But I know the total students must add to 82. So

$$ x+(x+.25x)+(x+9)=82 $$ Can you take it from there?