Question 1166276
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(j=w+n,j+p=k(w+p))}}}


{{{w+n+p=kw+kp}}}
{{{n+p=kw+kp-w}}}
{{{w(k-1)+kp=n+p}}}
{{{w(k-1)=n+p-kp}}}
{{{highlight(w=(n+p-kp)/(k-1))}}}


and to find j
{{{w=j-n}}}
substitute:
{{{j+p=k(j-n+p)}}}
{{{j+p=kj-kn+kp}}}
{{{kj-kn+kp=j+p}}}
{{{kj-kn+kp-j=p}}}
{{{kj-j=p+kn-kp}}}
{{{j(k-1)=p+kn-kp}}}
{{{highlight(j=(p+kn-kp)/(k-1))}}}



Whitney is 13, and John is   32     .