Word problem

Question

Translate into an equation.
The sum of two numbers is ten. The total of three times the smaller and twice the larger is twenty-two.
Find the two numbers.
Step 1
Use the variable x to denote the smaller number. Express the larger number in terms of the smaller number. Remember that their total is 10.

Answer 1

If the smaller number = x, then the larger number is 10 - x, since their total is 10. From the problem, we know that:

 

3x + 2(10 - x) = 22

3x + 20 - 2x = 22

x + 20 = 22

x = 2 = the smaller number

 

The larger number = 10 - x = 10 - 2 = 8