Question

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

Answer 1

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.