SOLUTION: John is 19 years older than Whitney. In 6 years John will be 2 times Whitney age. How old is each now?

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Question 1166276: John is 19 years older than Whitney. In 6 years John will be 2 times Whitney age. How old is each now?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
j John
w Whitney

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John is 19 years older than Whitney. In 6 years John will be 2 times Whitney age. How old is each now?
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The same type of question so often in the form of different examples.
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John is n years older than Whitney. In p years John will be k times Whitney's age. How old is each now?
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system%28j=w%2Bn%2Cj%2Bp=k%28w%2Bp%29%29

w%2Bn%2Bp=kw%2Bkp
n%2Bp=kw%2Bkp-w
w%28k-1%29%2Bkp=n%2Bp
w%28k-1%29=n%2Bp-kp
highlight%28w=%28n%2Bp-kp%29%2F%28k-1%29%29

and to find j
w=j-n
substitute:
j%2Bp=k%28j-n%2Bp%29
j%2Bp=kj-kn%2Bkp
kj-kn%2Bkp=j%2Bp
kj-kn%2Bkp-j=p
kj-j=p%2Bkn-kp
j%28k-1%29=p%2Bkn-kp
highlight%28j=%28p%2Bkn-kp%29%2F%28k-1%29%29


Whitney is 13, and John is 32 .

Answer by ikleyn(52793) About Me  (Show Source):
You can put this solution on YOUR website!
.
John is 19 years older than Whitney. In 6 years John will be 2 times Whitney age. How old is each now?
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In 6 years, two events will happen simultaneously:


   
    John will be 19 years older than Whitney  AND  John will be 2 times Whitney age.



It means that in 6 years John will be 38 years old, while Whitney will be 19 years old.


Hence, now they are 38-6 = 32 (John)  and  19-6 = 13 (Whitney) years old.   ANSWER

Solved.