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The difference between the present ages of two brothers is 6 years. If
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19 Apr 2023, 08:12
19 Apr 2023, 08:12
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The difference between the present ages of two brothers is 6 years. If after 4 years, the elder brother would be 3/2 times the age of the younger brother, what is the sum of their present ages?
8
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14
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22
8
10
14
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22
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: The difference between the present ages of two brothers is 6 years. If
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19 Apr 2023, 19:48
19 Apr 2023, 19:48
1
Expert Reply
According to the problem, e - y = 6.
In 4 years, the elder brother will be e + 4 years old, and the younger brother will be y + 4 years old.
The problem also tells us that, in 4 years, the elder brother will be 3/2 times the age of the younger brother:
e + 4 = (3/2)(y + 4)
We can simplify this equation by multiplying both sides by 2:
2e + 8 = 3y + 12
Now we can use the equation e - y = 6 to solve for e in terms of y:
e = y + 6
We can substitute this expression for e into the other equation:
2(y + 6) + 8 = 3y + 12
Simplifying:
2y + 20 = 3y + 12
y = 8
So the younger brother is currently 8 years old.
Using the equation e - y = 6, we can find that the elder brother is currently 14 years old.
Therefore, the sum of their present ages is 8 + 14 = 22.
Hence, the answer is 22.
In 4 years, the elder brother will be e + 4 years old, and the younger brother will be y + 4 years old.
The problem also tells us that, in 4 years, the elder brother will be 3/2 times the age of the younger brother:
e + 4 = (3/2)(y + 4)
We can simplify this equation by multiplying both sides by 2:
2e + 8 = 3y + 12
Now we can use the equation e - y = 6 to solve for e in terms of y:
e = y + 6
We can substitute this expression for e into the other equation:
2(y + 6) + 8 = 3y + 12
Simplifying:
2y + 20 = 3y + 12
y = 8
So the younger brother is currently 8 years old.
Using the equation e - y = 6, we can find that the elder brother is currently 14 years old.
Therefore, the sum of their present ages is 8 + 14 = 22.
Hence, the answer is 22.
gmatclubot
Re: The difference between the present ages of two brothers is 6 years. If [#permalink]
19 Apr 2023, 19:48
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