The examples below show the basic process in dealing with simple variables, or unknown quantities. To indicate an unknown, letters of the alphabet are used. The most frequent one is

**X**. To avoid confusion with the multiplication sign, the letter**Y**is used on this page. Do not include “Make an equation.” in your solution. Just think that.**Remember:**What you do on the one side of an equal sign, you must do on the other side.- You are 18 years old. You are 3 years older than your brother. How old is your brother?
- Let Y = the age of your brother.

*Make an equation.*

Y + 3 = 18

Y + 3 – 3 = 18 – 3

Y = 15

Your brother’s age = 15. - A mother is 5 times as old as her daughter. Their combined ages equal 36. How old is each person?
- Let Y = the age of the daughter.

Let 5Y = the age of her mother.*Make an equation.*

Y + 5Y = 36

6Y = 36

6Y ÷ 6 = 36 ÷ 6

Y = 6

The daughter’s age = 6

Her mother’s age = 30

- The sum of four consecutive numbers is 38. What are the numbers?
- Let the first number = Y.

Let the second number = Y + 1.

Let the third number = Y + 2.

Let the fourth number = Y + 3.*Make an equation.*

Y + Y + 1 + Y + 2 + Y + 3 = 38

4Y + 6 = 38

4Y + 6 – 6 = 38 – 6

4Y = 32

4Y ÷ 4 = 32 ÷ 4

Y = 8

The four consecutive numbers are 8, 9, 10, and 11.

When you become proficient, the steps may be modified a little. In this type of problem, it is better to let the smaller number be the unknown one. However, any of the numbers can be the unknown one.