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Hunter was one fifth as old as Erica, x years ago. In x years, Erica

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Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

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New post 17 Sep 2017, 03:24
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Question Stats:

80% (02:38) correct 20% (02:28) wrong based on 40 sessions

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Hunter was one fifth as old as Erica, x years ago. In x years, Erica will be twice as old as Hunter. What is the ratio of Hunter's current age to Erica's current age?

A. 11:15
B. 3:7
C. 5:13
D. 9:17
E. 7:23
[Reveal] Spoiler: OA

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Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

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New post 17 Sep 2017, 07:24
Let age of Erica after x years be E and Hunter's age be H.

From questions stem, E = 2H

Also,\(H - 2x = \frac{1}{5}(E - 2x) => 5H - 10x = E - 2x\)

Substituting the value of E, we will get \(3H = 8x => \frac{H}{x}= \frac{8}{3}\)

If H = 8, E = 16
2x(6) years ago, Hunter's age is 2 and that is one-fifth the age of Erica!

Since, we are asked for their current ages, it must be (8-3:16-3) or 5:13(Option C)
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Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

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New post 17 Sep 2017, 11:10
Hunter was one fifth as old as Erica, x years ago.
=> \((H-x)= \frac{1}{5}(E-x)\)
=> \(5H-5x= E-x\)
=> \(5H =E+4x\)

In x years, Erica will be twice as old as Hunter.
=> \(2(H+x)= E+x\)
=> \(2H+2x=E+x\)
=> \(2H=E-x\)

What is the ratio of Hunter's current age to Erica's current age: \(\frac{H}{E}\)????

=>\(5H =E+4x\)
=> \(x= \frac{5H-E}{4}\)

as \(2H=E-x\) => \(2H=E-\frac{5H-E}{4}\) => \(13H =5E\)
\(\frac{H}{E} = \frac{5}{13}\)

Answer: C

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Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

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New post 19 Sep 2017, 18:17
Bunuel wrote:
Hunter was one fifth as old as Erica, x years ago. In x years, Erica will be twice as old as Hunter. What is the ratio of Hunter's current age to Erica's current age?

A. 11:15
B. 3:7
C. 5:13
D. 9:17
E. 7:23

With elimination instead of substitution:

x years ago, Hunter was 1/5 as old as Erica

\(H - x = \frac{1}{5}(E - x)\)
\(5(H - x) = E - x\)
\(5H - 5x = E - x\)
\(5H = E + 4x\) ······ (A)

In x years, Erica will be twice as old as Hunter

\(2(H + x) = E + x\)
\(2H + 2x = E + x\)
\(2H = E - x\) ······· (B)

Looking at (A) and (B) . . . Multiply (B) by 4 (to eliminate x). Add it to (A).

\(8H = 4E - 4x\)
\(5H = E + 4x\)
----------------------
\(13H = 5E\)

Ratio of Hunter's current age to Erica's current age?

\(13H = 5E\)

\(\frac{H}{E} = \frac{5}{13}\)

ANSWER C

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Hunter was one fifth as old as Erica, x years ago. In x years, Erica   [#permalink] 19 Sep 2017, 18:17
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