CEMC Pascal, 2014

Algebra Difficulty 1.4 Junior Find the answer Canada

What number should go in the $\square$ to make the equation $\dfrac{3}{4} + \dfrac{4}{\square} = 1$ true?

Pick one

Solution

For $\dfrac{3}{4} + \dfrac{4}{\square} = 1$ to be true, we must have $\dfrac{4}{\square} = 1 - \dfrac{3}{4} = \dfrac{1}{4}$ .

Since $\dfrac{1}{4} = \dfrac{4}{16}$ , we rewrite the right side using the same numerator to obtain $\dfrac{4}{\square} = \dfrac{4}{16}$ .

Therefore, $\square = 16$ makes the equation true.

(We can check that $\dfrac{3}{4} + \dfrac{4}{16}=1$ , as required.)

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