Math CentralQuandaries & Queries


Question from kanesh, a student:




I think it is the fractions that may be causing you difficulties. In the first equation

\[\frac{p}{2} + \frac{q}{3} = 3\]

the denominators are 2 and 3. The number 6 is a multiple of both 2 and 3 so multiply both sides of the first equation by 6 and simplify. This will give you a new equation, equivalent to your first equation but with no fractions.

For the second equation

\[\frac{p}{4} + \frac{2q}{3}=3\]

what is a number that is a multiple of both 3 and 4. Multiply both sides by this number to obtain a new equation with no fractions.

Solve the resulting two equations. Make sure you verify your answer.


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