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The sum of the ages of a mother and her child is 63.
if the product of their ages four years ago was 484, what is their age now?
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If the sum of the ages of a mother and her child is 63 now,
hence, 4 years ago this sum was 63-4-4 = 55.
Next, 484 = (mentally) 4*121 = 2*2*11*11.
So, we should combine these factors to make a sum 55 from them.
For example, this way works
55 = 44 + 11 = (2*2*11) + 11,
so, we can assume that 4 years ago their age was 44 and 11;
so now their ages are 44+4 = 48 (mother) and 11+4 = 15. ANSWER
You may check that there no other solutions.
I leave this job to you, for your entertainment.
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Another way to solve it is to write this equation for their ages 4 years ago
x*(55-x) = 484
55x - x^2 = 484
x^2 - 55x + 484 = 0
and then solve it using the quadratic formula or factoring, on your choice.
