Question 1085934

Could you please explain how to tackle this problem?

The ratio of Jonathan’s age to David’s age is 6:5. In seven years it will be 7:6. What are their ages now.

Thanks in advance.
<pre>Let MULTIPLICATIVE factor of each person’s age be x
Then Jonathan’s age is: 6x and David’s is: 5x
We then get: {{{(6x + 7)/(5x + 7) = 7/6}}}
6(6x + 7) = 7(5x + 7) ---------- Cross-multiplying 
36x + 42 = 35x + 49
36x – 35x = 49 – 42
x, or MULTIPLICATIVE factor of each person’s age is 7
{{{highlight_green(matrix(2,5, "Jonathan’s", "age:", 6(7), "=", 42, "David’s", "age:", 5(7), "=", 35))}}}
It is that simple!!