The sum of two integers is thirty. Eight times the smaller integer is 6 more than 5 times the larger interger. Find the integers

First of all you must form equations. Now,

Let the smaller integer = x and

Let the greater integer = y

x + y = 30 ... (1) Given. The sum of the integers

8x = 5y + 6 or } Given. 8 times the smaller integer is

8x - 5y = 6 ... (2) } bigger by 6 than 5 times the greater

} integer.

(1) * 5, we get,

5x + 5y = 150 ... (3)

By adding Eq. (2) and (3),

13x = 156

So x = 156/13 = 12

By replacing this value of x in Eq. (1), we get

12 + y = 30

So y = 30 - 12 = 18

So, 12 and 18 are the integers.