Three different types of wine are $10\%, 12\%,$ and $14\%$ alcohol, respectively. If $a$ liters of the $10\%$

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

by M7MBA » Thu Oct 01, 2020 6:47 am

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Three different types of wine are $10\%, 12\%,$ and $14\%$ alcohol, respectively. If $a$ liters of the $10\%$ wine, $b$ liters of the $12\%$ wine, and $c$ liters of the $14\%$ wine are combined to form $a+b+c$ liters of an $11\%$ alcohol blend, then what is $a$ in terms of $b$ and $c?$

A. $b + 3c$

B. $c + 3b$

C. $2b + 3c$

D. $\dfrac{c + b}4$

E. $b + c$

Answer: A

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Thu Oct 01, 2020 6:47 am

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Re: Three different types of wine are $10\%, 12\%,$ and $14\%$ alcohol, respectively. If $a$ liters of the \(10\%\

by Scott@TargetTestPrep » Tue Oct 06, 2020 3:24 am

M7MBA wrote: ↑
Thu Oct 01, 2020 6:47 am
Three different types of wine are $10\%, 12\%,$ and $14\%$ alcohol, respectively. If $a$ liters of the $10\%$ wine, $b$ liters of the $12\%$ wine, and $c$ liters of the $14\%$ wine are combined to form $a+b+c$ liters of an $11\%$ alcohol blend, then what is $a$ in terms of $b$ and $c?$

A. $b + 3c$

B. $c + 3b$

C. $2b + 3c$

D. $\dfrac{c + b}4$

E. $b + c$

Answer: A

Solution:

We can create the equation:

0.1a + 0.12b + 0.14c = 0.11(a + b + c)

Multiplying the equation by 100, we have:

10a + 12b + 14c = 11a + 11b + 11c

b + 3c = a

Answer: A

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