Question 55

If $$a : b = 2 : 3$$, then $$\frac{3a + 4b}{4a + 5b}$$ is equal to:

Solution
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$$a : b = 2 : 3$$

Let's assume a = 2y and b = 3y.

$$\frac{3a + 4b}{4a + 5b}$$ = $$\frac{3\times2y+4\times3y}{4\times2y+5\times3y}$$

= $$\frac{6y+12y}{8y+15y}$$

= $$\frac{18y}{23y}$$

= 18 : 23

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