What number must be subtracted from each of 23, 30, 57 and 78 so that the four results are in proportion?

3Correct answerYour answer5Correct answerYour answer6Correct answerYour answer9Correct answerYour answer

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CorrectNot quiteAnswer C

Correct answer: C

Let the number be x. Then $(23 - x)(78 - x) = (30 - x)(57 - x)$ (product of extremes = product of means).
$1794 - 101x + x^2 = 1710 - 87x + x^2$ , so $84 = 14x$ and $x = 6$ .
Check: $17 : 24$ and $51 : 72$ are both $17 : 24$ .

Worth noting

Always check by substituting: with 6 the numbers become 17, 24, 51, 72, and $17 \times 72 = 24 \times 51 = 1{,}224$ .

Ten questions from Ratio & Proportion, at your own pace.

Explanation