I am stuck and unable to solve this using the single variable method. Please help.
5 years ago, Ebo was 3 times as old as Atu. In 3 years, Ebo will be twice as old as Atu. What is the sum o their ages now?
A) 18
B) 24
C) 28
D) 35
E) 42
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PS: Ages of Ebo and Atu
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Brent@GMATPrepNow
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Here's one approach:saadishah wrote:I am stuck and unable to solve this using the single variable method. Please help.
5 years ago, Ebo was 3 times as old as Atu. In 3 years, Ebo will be twice as old as Atu. What is the sum o their ages now?
A) 18
B) 24
C) 28
D) 35
E) 42
5 years in the PAST
Let A = Atu's age 5 years ago
So, 3A = Ebo's age 5 years ago
3 years in the FUTURE
A + 8 = Atu's age 3 years from now
3A + 8 = Ebo's age 3 years from now
In 3 years Ebo will be twice as old as Atu
This means that 3A + 8 is TWICE AS BIG AS A + 8
To make these values EQUAL, we'll multiply the smaller value by 2
We get: 3A + 8 = 2(A + 8)
Expand: 3A + 8 = 2A + 16
Solve, A = 8
5 years in the PAST
Atu's age 5 years ago = 8
So, Ebo's age 5 years ago = 24
So, their PRESENT ages are 13 and 29
SUM of present ages = 13 + 29 = 42
Aside: Here's a video solution that uses 2 variables- https://www.gmatprepnow.com/module/gmat- ... /video/909
Cheers,
Brent
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Hi saadishah,
While you can treat this as a one-variable question (as Brent has shown), this prompt is pretty easy to deal with as a 2-variable 'system.'
(E-5) = 3(A-5)
(E+3) = 2(A+3)
With 2 variables and 2 unique equations, you can solve for A and E.
Are you comfortable with the 2-variable approach (and were you just looking for an alternative?)?
GMAT assassins aren't born, they're made,
Rich
While you can treat this as a one-variable question (as Brent has shown), this prompt is pretty easy to deal with as a 2-variable 'system.'
(E-5) = 3(A-5)
(E+3) = 2(A+3)
With 2 variables and 2 unique equations, you can solve for A and E.
Are you comfortable with the 2-variable approach (and were you just looking for an alternative?)?
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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An alternate approach is to TEST CASES.5 years ago, Ebo was 3 times as old as Atu. In 3 years, Ebo will be twice as old as Atu. What is the sum of their ages now?
A) 18
B) 24
C) 28
D) 35
E) 42
5 years ago, Ebo was 3 times as old as Atu.
What is the sum of their ages now?
Case 1: Five years ago A=1 and E = 3*1 = 3
Sum of the their ages now = (1+5) + (3+5) = 14.
14 is not among the answer choices.
Case 2: Five years ago A=2 and E = 3*2 = 6
Sum of the their ages now = (2+5) + (6+5) = 18.
In 3 years, A = 7+3 = 10 and E = 11+3 = 14.
Since Ebo is not twice as old as Atu, eliminate A.
Case 3: Five years ago A=3 and E = 3*3 = 9
Sum of the their ages now = (3+5) + (9+5) = 22.
22 is not among the answer choices.
Notice the PATTERN:
The resulting sums -- 14, 18, 22 -- keep increasing by 4.
Thus, the correct sum must be in the following list:
14, 18, 22, 26, 30, 34, 38, 42...
Only the value in red is among the remaining answer choices.
The correct answer is E.
Last edited by GMATGuruNY on Sun Jul 24, 2016 7:54 pm, edited 1 time in total.
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You won't be able to solve it with a single variable since you have two, but you could think of it this way.
Five years ago, Ebo was (E - 5) and Atu was (A - 5). Back then, Ebo = 3 * Atu, so (E - 5) = 3 * (A - 5).
Three years from now, Ebo will be (E + 3) and Atu will be (A + 3). We'll then have Ebo = 2 * Atu, so (E + 3) = 2 * (A + 3).
The two equations simplify as
E = 3A - 10
E = 2A + 3
Both equations = E, so they equal each other: 3A - 10 = 2A + 3, or A = 13. From there, E = 2*13 + 3, or 29, and the sum of their ages is 42.
Five years ago, Ebo was (E - 5) and Atu was (A - 5). Back then, Ebo = 3 * Atu, so (E - 5) = 3 * (A - 5).
Three years from now, Ebo will be (E + 3) and Atu will be (A + 3). We'll then have Ebo = 2 * Atu, so (E + 3) = 2 * (A + 3).
The two equations simplify as
E = 3A - 10
E = 2A + 3
Both equations = E, so they equal each other: 3A - 10 = 2A + 3, or A = 13. From there, E = 2*13 + 3, or 29, and the sum of their ages is 42.
