Maria and her mother are shopping for a dress for Maria’s school dance. The dress Maria likes the most is $120. She asks her mom, “If I give you my cleaning money for the next six weeks, will you pay the other half?”
Maria is paid the same amount of money each week to clean her neighbor’s house. How can you use the information given here to determine how much money Maria earns each week?
In this concept, you will learn to solve and check single variable equations using mental math and substitution.
Solving Equations Using Mental Math
When working with an equation involving a single variable, you are looking for the number that gives a true statement when you replace the variable by the number. This process is referred to as solving the equation. The number that gives the true statement is said to “satisfy” the equation and is called the solution or root of the equation.
Let’s look at an example of solving an equation with a single variable.
You can solve this equation using mental math.
Then, add the numbers on the left side of the equals sign.
Let’s look at one more example.
Now multiply the numbers on the left side of the equals sign.
Earlier, you were given a problem about Maria and her new dress.
You want to know how much money Maria earns each week, if six weeks worth of pay is equal to half the cost of the $120 dress.
Then, ask yourself, “Six times what number equals 60?”
The answer is 10.
You can use mental math to solve this equation.
First, ask yourself, “What number subtract 6 equals 9?”
The answer is 15.
The answer is 5.
First, determine what the equation is asking you to find.
Then, divide 24 by 2 on the left side of the equals sign.
This is not a true statement.
Solve each equation using mental math. Be sure to check each answer by substituting your solution back into the original problem. Then simplify to see if the equation expresses a true statement.