Fractions/Ratios/Decimals

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Fractions/Ratios/Decimals

by swerve » Wed Apr 29, 2020 11:57 am

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A certain barrel is \(1/5\) full. When \(k\) liters of liquid are added to the barrel, it becomes \(2/3\) full. In terms of \(k\), what is the capacity of the barrel, in liters?

A. \(\dfrac{3}{8} k\)
B. \(\dfrac{7}{15} k\)
C. \(\dfrac{15}{7} k\)
D. \(\dfrac{7}{3} k\)
E. \(\dfrac{8}{3} k\)

The OA is C

Source: Magoosh
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Re: Fractions/Ratios/Decimals

by Scott@TargetTestPrep » Fri May 01, 2020 3:12 pm
swerve wrote:
Wed Apr 29, 2020 11:57 am
A certain barrel is \(1/5\) full. When \(k\) liters of liquid are added to the barrel, it becomes \(2/3\) full. In terms of \(k\), what is the capacity of the barrel, in liters?

A. \(\dfrac{3}{8} k\)
B. \(\dfrac{7}{15} k\)
C. \(\dfrac{15}{7} k\)
D. \(\dfrac{7}{3} k\)
E. \(\dfrac{8}{3} k\)

The OA is C

Source: Magoosh
We can let T = the capacity of the barrel and create the equation:

T/5 + k = 2T/3

Multiplying by 15, we have:

3T + 15k = 10T

15k = 7T

15k/7 = T

Answer: C

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