Which smallest positive number should be subtracted from each of 9 and 13 so that 18 is the third proportion to them?
Answer & explanation
Correct answer: option 4
Let the required number be x
Then, 9 - x : 13 - x :: 13 - x : 18
18 = \(\frac{(13-x)²}{9-x}\)
18(9 - x) = (13 - x)²
162 - 18x = x² - 26x + 169
x² - 8x + 7 = 0
Solving,
x = 1, 7
smallest positive number is 1