Question

Tom and Alison are both salespeople. Tom’s weekly compensation consists of $ 300 $ plus on $ 20 $ percent of his sales. Alison’s weekly compensation consists of $200$ pluson $ 25 $ percent of her sales. If they both had the same amount of sales and the same compensation for a particular week, that was that compensation, in dollars?
(Disregard the dollar sign when gridding your answer)
A. $ 600 $
B. $ 700 $
C. $ 750 $
D. $ 650 $

Answer 1

Hint: Consider their sells to be equal to $ x $ and their compensation to be equal to $ y. $ Then convert the word problem into mathematical equations in terms of $ x $ and $ y $ , Solve the two equations obtained from given two conditions to find the values.

Complete step-by-step answer:
Let the number of sells done by both of them in a particular week be $ x $
Let the compensation received by both of them for that week be $ y $
Then, Tom’s compensation (in dollar) will be
 $ y = 300 + \dfrac{{20x}}{{100}}. $
By simplifying, we get
 $ \Rightarrow y = 300 + \dfrac{x}{5} $
Multiplying both the sides by 5 we get
 $ 5y = 1500 + x $
Rearranging it, we get
 $ 5y - x = 1500 $ . . . (1)
Alison’s compensation will be given by
 $ y = 200 + \dfrac{{25x}}{{100}} $
 $ \Rightarrow y = 200 + \dfrac{x}{4} $
Multiplying both the sides by 4 we get
 $ 4y = 800 + x $
By rearranging the equation, we get
 $ 4y - x = 800 $ . . . (2)
Subtracting equation (2) from equation (1), we get
 $ y = 700 $
Therefore, Tom and Alison received the compensation of \[\ $ 700\]
Therefore, from the above explanation the correct answer is, option (B) $ 700. $

So, the correct answer is “Option B”.

Note: Using the statement compensation in dollars didn’t affect the solution as the information given was in dollars. But if it was asked to find the compensation in any other currency like rupees. Then this would have changed our final answer as we would have needed to convert the dollar into rupees.
Since we were asked to find compensation only, we simplified our equations in such a way that the term $ x $ would get cancelled and our time would be saved.