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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.

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  • $\begingroup$ HINT: $y-x=t$ where $t$ represents tax paid, you want to calculate $$\frac tx$$ $\endgroup$
    – WW1
    Aug 10, 2018 at 23:54

1 Answer 1

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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

$$1-\frac{a}{b}.$$

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