Maths Olympiad Prep

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Problem 248

Algebra Difficulty 1.5 Find the answer CEMC Pascal

What number should go in the □\square to make the equation 34+4□=1\frac{3}{4}+\frac{4}{\square}=1 true?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

For 34+4□=1\frac{3}{4}+\frac{4}{\square}=1 to be true, we must have 4□=1−34=14\frac{4}{\square}=1-\frac{3}{4}=\frac{1}{4}. Since 14=416\frac{1}{4}=\frac{4}{16}, we rewrite the right side using the same numerator to obtain 4□=416\frac{4}{\square}=\frac{4}{16}. Therefore, □=16\square=16 makes the equation true.

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