The sum of two integers is twenty-five. Seven times the smaller integer is seven more than five times the larger integer. Find the integers. (If there is no solution, enter NO SOLUTION.)

Question

The sum of two integers is twenty-five. Seven times the smaller integer is seven more than five times the larger integer. Find the integers. (If there is no solution, enter NO SOLUTION.)

Answer 1

S+L=25

S = 25-L

7S= 7 + 5L

7(25-L) = 7+5L

175 - 7L = 7+5L

12L = 175-7= 168

L = 168/12 = 14

S = 25-L = 25-14 = 11

small is 11, large is 14