Toshi is four times as old as Kosuke. In \(x\) years Toshi will be three times as old as Kosuke. How old is Kosuke, in

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Toshi is four times as old as Kosuke. In \(x\) years Toshi will be three times as old as Kosuke. How old is Kosuke, in terms of \(x?\)

(A) \(2x\)
(B) \(3x\)
(C) \(4x\)
(D) \(8x\)
(E) \(12x\)

Answer: A

Source: Manhattan GMAT

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VJesus12 wrote:
Tue Sep 15, 2020 2:18 am
Toshi is four times as old as Kosuke. In \(x\) years Toshi will be three times as old as Kosuke. How old is Kosuke, in terms of \(x?\)

(A) \(2x\)
(B) \(3x\)
(C) \(4x\)
(D) \(8x\)
(E) \(12x\)

Answer: A

Source: Manhattan GMAT
Toshi is four times as old as Kosuke.
Let K = Kosuke's PRESENT age
So, 4K = Toshi's PRESENT age

Note: This also means....
K + x = Kosuke's age IN x YEARS
4K+ x = Toshi's age IN x YEARS


In x years Toshi will be three times as old as Kosuke.
In other words: (Toshi's age IN x YEARS) = 3(Kosuke's age IN x YEARS)
We can write: 4K+ x = 3(K+ x)

How old is Kosuke, in terms of x?
In other words, we want Kosuke's PRESENT age (K) in terms of x
Take: 4K+ x = 3(K+ x)
Expand the left side: 4K + x = 3K + 3x
Subtract 3K from both sides: K + x = 3x
Subtract x from both sides: K = 2x

So, Kosuke's PRESENT age = 2x

Answer: A

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VJesus12 wrote:
Tue Sep 15, 2020 2:18 am
Toshi is four times as old as Kosuke. In \(x\) years Toshi will be three times as old as Kosuke. How old is Kosuke, in terms of \(x?\)

(A) \(2x\)
(B) \(3x\)
(C) \(4x\)
(D) \(8x\)
(E) \(12x\)

Answer: A

Solution:

If we let Kosuke’s current age = K, then Toshi’s current age = 4K. In x years, we have:

4K + x = 3(K + x)

4K + x = 3K + 3x

K = 2x

Answer: A

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