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# John is twice as old as his son and three times as old as his daughter

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Manager
Joined: 18 Jul 2019
Posts: 54
John is twice as old as his son and three times as old as his daughter  [#permalink]

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25 Nov 2019, 06:19
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John is twice as old as his son and three times as old as his daughter. Find the ratio of John’s age to his son’s age when John’s age becomes twice that of his daughter age.

a) 7/4
b) 7/5
c) 8/5
d) 9/4
e) 9/8
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: John is twice as old as his son and three times as old as his daughter  [#permalink]

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26 Nov 2019, 18:32
CaptainLevi wrote:
John is twice as old as his son and three times as old as his daughter. Find the ratio of John’s age to his son’s age when John’s age becomes twice that of his daughter age.

a) 7/4
b) 7/5
c) 8/5
d) 9/4
e) 9/8

$$J=2s=3d$$
Say after x years J becomes 2 of d...$$J+x=2(d+x)...3d+x=2d+2x.....d=x$$
This means J=3x, and 2s=3x

The age of J and s after x years will be $$J+x=3x+x=4x$$, and $$s+x=\frac{3x}{2}+x=\frac{5x}{2}$$

RAtio = $$4x:5x/2=8x:5x=8:5$$

C
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Re: John is twice as old as his son and three times as old as his daughter  [#permalink]

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28 Nov 2019, 17:37
CaptainLevi wrote:
John is twice as old as his son and three times as old as his daughter. Find the ratio of John’s age to his son’s age when John’s age becomes twice that of his daughter age.

a) 7/4
b) 7/5
c) 8/5
d) 9/4
e) 9/8

We can let John be 60 years old currently; thus, his son is 30 years old, and his daughter is 20 years old. Next we can let x = the number of years from now such that John will be twice his daughter’s age and create the equation:

60 + x = 2(20 + x)

60 + x = 40 + 2x

20 = x

Therefore, in 20 years, John will be twice his daughter’s age (in fact, John will be 80 years old, and his daughter will be 40 years old). At that time, his son will be 50 years old; therefore, the ratio of John’s age to his son’s age will be 80/50 = 8/5.

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Re: John is twice as old as his son and three times as old as his daughter   [#permalink] 28 Nov 2019, 17:37
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