Question

Remo, who works in a high end jewellery store, earns a base pay of $\$10.00$ per hour plus a certain percent commission on the sales that he helps to broker in the store. Remo worked an average of 35 hours per week over the past two weeks and helped to broker sales of $\$5,000.00$ worth of jewellery during that same two week period. If Remo’s earnings for the two week period were $\$850.00$, what percent commission on sales does Remo earn?
A. 1%
B. 2%
C. 3%
D. 4%

Answer 1

Hint: Use the fact that Remo earns a base pay of $\$10.00$ per hour to find the total base amount paid to him after he worked for an average of 35 hours per week over the two week period. Then by using the difference between his total earnings and the total base amount earned, find the commission amount earned by Remo. In the end, determine what percent of the sales amount ($\$5,000.00$) is the commission amount.

Complete step by step answer:
First, we see that Remo earns a base pay of $\$10.00$ per hour. Then the total base amount paid to him after he worked an average of 35 hours in a week over the two week period would be
$\text{Total base amount earned}=2\cdot 35\cdot \$10=\$700.00$
Now, we observe that his total earnings over the two week period is $\$850.00$ then, the commission amount can be found by subtracting the total base amount from his total earnings.
$\text{Total commission amount}=\$850-\$700=\$150.00$
It remains to find what percent of the sales brokered by Remo over the two week period ($\$5,000.00$) is $\$150.00$, we assume this percentage to be $x\%$ . Then
$x\%\cdot 5,000=150\Rightarrow \dfrac{x}{100}\cdot 5,000=150$
Now, we rearrange the equation to solve for $x$ .
$\dfrac{x}{100}\cdot 5,000=150\Rightarrow x=\dfrac{15,000}{5,000}=3\%$

So, the correct answer is “Option C”.

Note: Observe that the question provides the average number of hours Remo worked per week over a two week period. A common mistake is to calculate the total base amount earned by him without taking into account the factor of 2 that must be multiplied to the base amount because of the two week period. Furthermore, note that it is always reasonable to assume an unknown figure as a variable ( $x$ in this case) to simplify calculations.