Word Problem

Question

One number is 11 less than another. If their sum is increased by eight, the result is 81. Find the numbers.

How do I solve this problem step by step?

Answer 1

We can call the first number x, and the second number y.

 

Based on the first sentence, x = y-11.

 

Based on the second, (x + y) + 8 = 81. Because this is addition, we can remove the parentheses.

 

With two equations, we can solve for x and y.

 

x = y - 11

x + y + 8 = 81

 

To do this, I will replace the x in the second equation with "y-11"

 

(y - 11) + y + 8 = 81

y - 11 + y + 8 = 81

 

Combine like terms

2y - 3 = 81

 

Add 3 to both sides.

2y = 84

 

Divide both sides by 2

y = 42

 

x = y - 11

x = 42 - 11

x = 31

 

We can test to see if our answer is correct by inserting these numbers into the second equation:

31 + 42 + 8 = 81

81 = 81

 

x = 31, and y = 42