GMAT Practice Question: Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will...
Question
Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only 500USD more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals 60,000USD, what is the largest bonus Agnes can receive?
- 3,25USD
- 3,325USD
- 3,400USD
- 3,475USD
- 3,500USD
Topics: word problems, linear equations, translations
Solution
Step 1
We name the bonus for Agnes as A and the bonus for Cheryl as C.
A = \text{bonus for Agnes} C = \text{bonus for Cheryl}
Step 2
We translate \textbf{\text{"only 500USD more than Cheryl will receive"}} into an equation.
A = C + 500
Step 3
We interpret \textbf{\text{"None of the employees will receive a smaller bonus than Cheryl"}}, so to make Agnes's bonus as large as possible, we assign each of the other 18 employees exactly C.
\text{Each of the other 18 bonuses} = C
Step 4
We translate \textbf{\text{"totals 60,000USD"}} into an equation for all bonuses.
A + C + 18C = 60000
Step 5
We substitute the expression for A into the total and simplify to isolate C.
(C + 500) + 19C = 60000 20C + 500 = 60000
Step 6
We subtract 500 from both sides and divide by 20 to find C.
20C = 60000 - 500 = 59500 C = \frac{59500}{20} = 2975
Step 7
We add 500 to Cheryl's bonus to find Agnes's bonus.
A = 2975 + 500 = 3475
Answer
3475 USD
