Question

two consecutive even numbers are such that half of the larger number exceeds one fourth of the smaller number by 5 then the larger number is​

Answer 1

Step-by-step explanation:

Let x and (x+2) be the two consecutive even numbers. Where (x + 2) > x

Therefore, according to the given information:

$\frac{1}{2} (x + 2) = \frac{1}{4} x + 5 \\ \implies \: \frac{x + 2}{2} = \frac{x}{4} + 5\\ \implies \: \frac{x + 2}{2} = \frac{x + 4 \times 5}{4} \\ \implies \: \frac{x + 2}{2} = \frac{x + 20}{4} \\ \implies \: \frac{x + 2}{1} = \frac{x + 20}{2} \\ \implies \: 2(x + 2) = x + 20 \\ \implies \: 2x + 4 = x + 20 \\ \implies \:2x - x = 20 - 4 \\ \implies \: \huge \: { x = 16}\\ \therefore \: x + 2 = 16 + 2 = 18\\ Hence \: number\:larger \: is \: 18.$