A family paid 12 percent of its annual after-tax income on food last year. This amount was equal to 10 percent of its annual before-tax income last year. Which of the following is closest to the percent of the family's annual before-tax income that was paid for taxes last year?
A. 8% B. 12% C. 17% D. 20% E. 25%
My thoughts are set the after-tax income as x and before-tax income as y, then 0.12x = 0.10y, meaning y = 1.2x. And here is where I got stuck, please help me with this problem.
Let $a$ be the after-tax income. Then
$$\frac{12}{100}a$$
is the after-tax income spent on food.
Let $b$ be the before-tax income. Then
$$\frac{10}{100}b=\frac{12}{100}a.$$
You need to find
$$1-\frac{a}{b}.$$