Question

If the lesser of the two consecutive even integers is five more than half the greater, what are the two integers?

Answer 1

The integers are 12, 14.

Solution:

Let the even consecutive integers be x and x + 2.

Lesser number = x and Greater number = x + 2

Lesser number = Half of greater number + 5

$\Rightarrow x = \frac{1}{2} (x + 2) + 5$

$\Rightarrow x = \frac{x + 2}{2} + 5$

To add the numbers, denominators must be same. So multiply 5 by $\frac{2}{2}$.

$\Rightarrow x = \frac{x + 2}{2} + \frac{10}{2}$

$\Rightarrow x = \frac{x + 12}{2}$

Multiply by 2 on both sides, we get

⇒ 2x = x + 12

Subtract x from both sides.

⇒ x = 12

Lesser number = 12

Greater number = 12 + 2 = 14

Hence the integers are 12, 14.