Question 57

What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)?

Solution

If x is added to each of numbers, the numbers so obtained in this order are in proportion

so, $$\frac{10 + x}{16 + x} = \frac{22 + x}{32 + x}$$

(10 + x)(32 + x) = (16 + x)(22 + x)

320 + 10x + 32x + $$x^2 = 352 + 16x + 22x + x^2$$

320 + 42x = 352 + 38x

4x = 32

x = 8

(x + 1) = 8 + 1 = 9

(3x + 1) = 24 + 1 = 25

Mean proportional = $$\sqrt{9 \times 25}$$ = 15

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