A restaurant buys fruit in cans containing $3\frac12$ cups of fruit each. If the restaurant uses $\dfrac12$ cup of

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun Jan 31, 2021 1:27 pm

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A restaurant buys fruit in cans containing $3\frac12$ cups of fruit each. If the restaurant uses $\dfrac12$ cup of the fruit in each serving of its fruit compote, what is the least number of cans needed to prepare $60$ servings of the compote?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 12

Answer: C

Source: GMAT Paper Tests

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Source: Beat The GMAT — Problem Solving | Sun Jan 31, 2021 1:27 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: A restaurant buys fruit in cans containing $3\frac12$ cups of fruit each. If the restaurant uses $\dfrac12$ cup

by deloitte247 » Wed Feb 03, 2021 12:06 am

$$There\ are\ 3\frac{1}{2}\ cups\ per\ can$$
$$restaurant\ uses\ \frac{1}{2}cup\ of\ fruit\ per\ serving$$
$$so\ if\ \frac{1}{2}cup\ =\ 1\ serving\ then,$$
$$x\ cups\ =\ 60\ serving$$
$$x=60\ \cdot\ \frac{1}{2}=30\ cups\ per\ serving$$
$$if\ \ 3\frac{1}{2}\ cups\ =\ 1\ can\ then,$$
$$30\ cups\ =\ x\ cans$$
$$x=\frac{30}{3\frac{1}{2}}=\frac{30}{\frac{7}{2}}=30\cdot\frac{2}{7}$$
$$x=\frac{60}{7}=8.6\approx9\ cans$$
$$Answer\ =\ C$$

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