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# Beth is 12 years younger than Alan. In 20 years, Beth will b

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Beth is 12 years younger than Alan. In 20 years, Beth will b [#permalink]  14 Jun 2018, 14:29
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Question Stats:

100% (01:20) correct 0% (00:00) wrong based on 16 sessions
Beth is 12 years younger than Alan. In 20 years, Beth will be 80% of Alan’s age. How old is Beth now?

[Reveal] Spoiler: OA
28

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Re: Beth is 12 years younger than Alan. In 20 years, Beth will b [#permalink]  15 Jun 2018, 01:25
B+12=A
B+20=0.8(A+20)
B+20=0.8(B+12+20)
B+20=0.8B+25.6
B=28
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2976 [0], given: 394

Re: Beth is 12 years younger than Alan. In 20 years, Beth will b [#permalink]  05 Jul 2018, 01:50
Expert's post
Explanation

Since Beth is 12 years younger than Alan, you can write:

$$B = A - 12$$

To translate “in 20 years, Beth will be 80% of Alan’s age,” make sure that Beth becomes B + 20 and Alan becomes A + 20 (if you will be doing other operations to these values, put parentheses around them to make sure the rules of PEMDAS are not violated):

$$B + 20 = 0.8(A + 20)$$

$$B + 20 = 0.8A + 16$$

$$B + 4 = 0.8A$$

Since the first equation is already solved for B, plug (A – 12) into the simplified version of the second equation in place of B:

$$B + 4 = 0.8A$$

$$(A - 12) + = 0.8A$$

$$A - 8 = 0.8A$$

$$0.2A - 8 = 0$$

$$0.2A = 8$$

$$A = 40$$

Alan is 40. Since B = A – 12, Beth is 28.

Check the answer. In 20 years, Beth will be 48 and Alan will be 60, and it is true that 48 is 80% of 60.

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Re: Beth is 12 years younger than Alan. In 20 years, Beth will b [#permalink]  10 Jul 2018, 03:07
We have system of equations: B+12=A and B+20=4/5*(A+20) -> A+8=4/5*(A+20) -> A=40 -> B=40-12=28.
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Re: Beth is 12 years younger than Alan. In 20 years, Beth will b   [#permalink] 10 Jul 2018, 03:07
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