Finding price when given percentage sales tax

Striver wrote:Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

A) $368
B) $380
C) $400
D) $420
E) $432

Let us assume that purchase price = $P
8% of P = 0.08P = Tax on purchase price
If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase.
So, 0.05P = 0.08P - 12
12 = 0.03P
P = 12/0.03
P = 400

So, we get the purchase price as $400.
Now, 8% of $400 = 0.08 * 400 = $32
Therefore, the total amount that Connie paid for her purchase including sales tax = $400 + $32 = [spoiler]$432[/spoiler]

The correct answer is E.

Striver wrote: ↑

Wed May 30, 2012 4:51 pm

Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

A) $368
B) $380
C) $400
D) $420
E) $432

Let's start with the following word equation: (total cost including 8% tax) - (total cost including 5% tax) = $12

Let x = the cost of the purchase (without tax)

So we can write: (x + 8% of x) - (x + 5% of x) = $12
In other words: (x + 0.08x) - (x + 0.05x) = $12
Simplify: 0.03x = 12
Solve: x = 12/0.03 = 1200/3 = 400

So, the cost of the purchase (without tax) is $400

So, the total amount Connie paid = $400 + (8% of $400) = $432

Answer: E