Question 62371
<b>John's present age is three-fourths of Sally's present age. In five years, John's age will be four-fifths of Sarah's age at that time. What are the present ages of John and Sally?</b>

The two equations are:
{{{J=(3/4)S}}}.
{{{J+5=(4/5)(S+5)}}}.

Replace J with (3/4)S in the 2nd equation:
{{{(3/4)S+5=(4/5)(S+5)}}}.
Multiply both sides of the equation by 20 to get rid of the fractions:
{{{15S+100=16(S+5)}}}.
Or, {{{15S+100=16S+80}}}.
Or, {{{100=S+80}}}.

So, {{{S=20}}}. 
Sally is 20 years old. John is 3/4 of Sally's age so John is 15.

Verification:
In 5 years Sally will be 25 and John will be 20 which is indeed four-fifth's of Sally's age in 5 years.