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

This topic has expert replies
Legendary Member
Posts: 1137
Joined: 14 Oct 2017
Followed by:3 members

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

by VJesus12 » Tue Sep 15, 2020 2:18 am

00:00

A

B

C

D

E

Global Stats

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) $$12x$$

Source: Manhattan GMAT

GMAT/MBA Expert

GMAT Instructor
Posts: 15003
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1265 members
GMAT Score:770

Re: Toshi is four times as old as Kosuke. In $$x$$ years Toshi will be three times as old as Kosuke. How old is Kosuke,

by Brent@GMATPrepNow » Tue Sep 15, 2020 6:09 am
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) $$12x$$

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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
If you enjoy my solutions, I think you'll like my GMAT prep course

Watch these video reviews of my course
And check out these free resources

GMAT/MBA Expert

GMAT Instructor
Posts: 5531
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:24 members

Re: Toshi is four times as old as Kosuke. In $$x$$ years Toshi will be three times as old as Kosuke. How old is Kosuke,

by Scott@TargetTestPrep » Thu Sep 24, 2020 7:09 am
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) $$12x$$

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