Math CentralQuandaries & Queries


Question from Naryn, a student:

Question 1.

(1÷x) + (1÷y) = (7÷12)
xy = 12

Hi Naryn,

If you express the left side with a common denominator of $xy$ you get

\[\frac{y + x}{xy} = \frac7{12}\]

but $xy = 12$ so do you know two numbers with product is $12$ and sum $7?$

The problem with this solution is that you don't know if this is the only correct answer. A better approach is to solve $xy = 12$ for $y$ and substitute into the first equation. Now adding the two fractions on the left side of this equation and simplifying gives you a quadratic equation you can solve for $x.$


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