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
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