HolaMaven wrote:

Maria pays \(\frac{1}{8}\) of her monthly income for food, \(\frac{1}{8}\) for utilities, \(\frac{1}{8}\) for student loans, and \(\frac{4}{5}\) of the remainder for rent. If at the end of each month Maria puts \(\frac{1}{2}\) of her remaining income into a CD account, what portion of her monthly income does she puts into the account?

A. \(\frac{1}{8}\)

B. \(\frac{1}{10}\)

C. \(\frac{7}{80}\)

D. \(\frac{1}{16}\)

E. \(\frac{1}{20}\)

I think

HolaMaven 's approach is the quickest. IMO this problem's challenge is to be meticulous regardless of approach. Easiest for me after reading the prompt: track on what remains after each deduction.

1) What portion is left after Maria pays for food, utilities, and loans? Each is \(\frac{1}{3}\) of her total monthly income ( = 1).

1 - [3 * \((\frac{1}{8})\)]

1 - \(\frac{3}{8}\)= \(\frac{5}{8}\) remains

2) Rent = \(\frac{4}{5}\) of the remaining \(\frac{5}{8}\) -- what portion is left after she pays rent?

\(\frac{5}{8}\) -\((\frac{4}{5}\) *\(\frac{5}{8})\) =

\(\frac{5}{8}\) - \(\frac{1}{2}\) = \(\frac{1}{8}\) remaining

3) CD = \(\frac{1}{2}\) of the remaining \(\frac{1}{8}\)

\(\frac{1}{2}\) * \(\frac{1}{8}\) = \(\frac{1}{16}\)

\(\frac{1}{16}\) is the portion of her monthly income that goes to her CD account

Answer D

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