Question

the sum of two numbers is 21 if 8 less than the sum of the two numbers is 5 more than triple the smaller number find the two numbers

Answer 1

x + y = 21

x + y - 8 = 3*y + 5

Subtract y from both sides.

x - 8 = 3y - y + 5

x - 8 = 2y + 5 Substitute x = 21 - y into the equation

21 - y - 8= 2y + 5

13 = 3y + 5 Subtract 5 from both sides

13 - 5 = 3y

8 = 3y Divide by 3

y = 8/3

x + y = 21

x + 8/3 = 21

x = 21 - 8/3

x = 18 1/3 or 18.333333

Check

The smaller number is 8/3

x + y - 8 = 3*(8/3) + 5 Remember that x + y = 21

21 - 8 = 8 + 5

13 = 13 and they check. Which one is the smaller number does not become a factor until you check your answer.