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.
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.
