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Question 4

The natural number which is subtracted from each of the four numbers $$17, 31, 25, 47$$ to give four numbers in proportion is

Solution

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Let $$k$$ be the number subtracted, so $$\frac{17-k}{31-k}=\frac{25-k}{47-k}$$. Cross multiplying gives $$799-64k=775-56k$$, so $$24=8k$$, giving $$k=3$$.

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