Question

A:b = 5:2. what is the value of (8a + 9b): (8a + 2b)?

Answer 1

guess a=5x ; b=2x

   (8a+9b) : (8a+2b)
=8a+9b / 8a+2b
=8×5x + 9×2x /  8×5x + 2×2x
=40x+18x / 40x+4x
=2x(20+9) / 4x(10+1)
=1× 29 / 2 ×11
=29/22

Answer 2

Concept

The ratio is a measure of how much of one quantity is present in the other. The common form for expressing the ratio of two quantities, "a" and "b", is a: b, which is read as "a is to b". The fractional format for this ratio is a / b. For further simplification, follow the same steps for ratios that you use to simplify fractions. a:b = a/b.

Given

We have given a ratio a : b = 5 : 2

Find

We are asked to determine the ratio of (8a + 9b): (8a + 2b) .

Solution

Let the ratio be  $a:b=5:2$ be equals to x.

$\frac{a}{b} =\frac{5x}{2x}$

Putting a = 5x and b = 2x in (8a + 9b): (8a + 2b) , we get

$\frac{8a+9b}{8a+2b} = \frac{8(5x)+9(2x)}{8(5x)+2(2x)}\\\\=\frac{40x+18x}{40x+4x}\\\\=\frac{58x}{44x} \\\\=\frac{29}{22}$

Therefore, the value of  (8a + 9b): (8a + 2b) is 29/22

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