Problem Solving

what's an easy way to set this up using plugging in?

jzw wrote:what's an easy way to set this up using plugging in?

We can REASON our way to the correct answer.
The tax rates are 8% and 5%.
The answer choices are all integers.
Thus, the base price is likely a multiple of 100; otherwise, the two taxes will not be integers.

If the base price = 400:
8% tax = .08(400) = 32.
5% tax = .05(400) = 20.
32-20 = 12.
Success! The 8% tax is $12 more than the 5% tax.

Thus, the base price with 8% tax = 400+32 = 432.

The correct answer is E.

Algebraically:
Reducing the tax by 3% lowers the price by $12.
Thus, the $12 difference must be 3% of the base price:
.03(x) = 12.
x = 12/(.03) = 1200/3 = 400.
Thus, the base price with 8% tax = 400 + .08(400) = 432.