Problem Solving

BTGmoderatorDC wrote: ↑

Mon Aug 29, 2022 11:13 pm

In her position as a real estate agent, Sarah receives a bonus for each sale she makes. Last week, she earned a $4,000 bonus, which decreased her average bonus amount to $4800. If this represents a decrease of 4%, how many sales has Sarah made?

A 4
B. 5
C. 8
D. 16
E. 25


OA B

Source: Veritas Prep

Last week, Sarah earned a $4,000 bonus, which decreased her average bonus amount to $4800. This represents a decrease of 4%.
Let x = OLD average bonus amount
We can write: x - 0.04x = $4800
Simplify: 0.96x = $4800
Solve: x = $4800/(0.96) = $5000

How many sales has Sarah made?
Let n = the TOTAL number of sales that Sarah has made.
This means (n-1) sales had an average bonus amount of $5000, and 1 sale had an bonus amount of $4000
All of this results in an AVERAGE bonus amount of $4800
We can write: [(n-1)($5000) + (1)($4000)]/n = $4800
Multiply both sides by n to get: (n - 1)(5000) + (1)(4000) = 4800n
Expand: 5000n - 5000 + 4000 = 4800n
Simplify: 5000n - 1000 = 4800n
Solve: n = 5

Answer: B