Question

Tom and Alison are both salespeople. Toms weekly compensation consists of $\$300$ plus $20$ percent of his sales. Alisons weekly compensation consists of $\$200$ plus $25$ percent of her sales. If they both had the same amount of sales and the same compensation for a particular week, what was that compensation, in dollars? (Disregard the dollar sign when gridding your answer.)

• A. $600$
• B. $700$
• C. $750$
• D. $650$

Answer 1

Answer: (B)

Let’s use $x$ for sales in dollars. Tom’s compensation (in dollars) will be $300+0.20x$. Alison’s compensation will be $200+0.25x$. To find $x$, set them equal to each other.

$300+0.20x=200+0.25x$
$100=0.06x$
$2000=x$

Now remember, the question didn’t ask you for their total sales! It asked you for their total compensation! Now that you know the sales, you have one more step to answer the question: use one side of the equation above to figure out what each person made that week.

I’m going to use Tom’s:

$300+0.20\left(2000\right)=700$