Math CentralQuandaries & Queries


Question from Angel:

The sum of Keith's age and Alan's age is 36. Four years ago, the ratio of Keith's age to Alan's age was 4:3. Find the ratio of their present age

Hi Angel,

I would solve for Keith's and Alan's present ages and then calculate the ratio.

Suppose Keith's current age is $k$ years and Alan's current age is $a$ years. You know that

\[k + a = 36.\]

How old was Keith 4 years ago? How old was Alan 4 years ago? What was the ratio of their ages 4 years ago? You know this ratio is 4:3 so this gives you a second equation. Write this equation in terms of fractions rather than ratios.

You now have two equations on $k$ and $a.$ Solve for $k$ and $a.$

write back if you need more assistance,

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