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

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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

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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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