Question 1170973

The sum of the ages for Peter and Paul is 24. Five years ago their respective ages were in the ratio 3:4. How old will they be in three years time?
<pre>Let Peter's age be P
Then Paul's is: 24 - P
We then get: {{{matrix(2,3, (P - 5)/(24 - P - 5), "=", 3/4, (P - 5)/(19 - P), "=", 3/4)}}}
4(P - 5) = 3(19 - P) ------ Cross-multiplying 
4P - 20 = 57 - 3P
4P + 3P = 57 + 20
7P = 77
Peter or {{{highlight_green(matrix(1,6, P, "=", 77/7, "=", 11, years-old))}}}
Paul's age: {{{highlight_green(matrix(1,3, 24 - 11, "=", 13))}}}
Can you now find their ages, 3 years from now?