### Let’s Think About It

Lisa's older sister Theresa has agreed to loan Lisa some money so Lisa can buy a new pair of jeans. Theresa is going to charge Lisa interest until Lisa pays her back. Theresa tells Lisa that she will calculate how much interest Lisa owes after

months according to the expression where is the cost of the jeans. Lisa wants to figure out how much interest she will owe Theresa if the jeans cost $60 and she doesn't pay Theresa back for 3 months.In this concept, you will learn how to evaluate expressions with more than one variable.

### Guidance

A **variable** is a symbol or letter (such as or ) that is used to represent a quantity that might change in value. A **variable expression** is a mathematical phrase that contains numbers, operations, and variables.

Here are some examples of variable expressions:

You can use a variable expression to describe a real world situation where one or more quantities has an unknown value or can change in value.

To **evaluate** a variable expression means to find the value of the expression for given values of the variables. To evaluate, substitute the given values for the variables in the expression and simplify using the order of operations. To follow the order of operations, you always need to do any multiplication/division first before any addition/subtraction.

Here is an example.

Evaluate the expression

if and .First, substitute 2 in for the letter

and 4 in for the letter in the expression.

Notice that you can put parentheses around the numbers to keep them separate and to indicate multiplication.

Now, simplify the expression using the order of operations. You will need to multiply first and then add.

The answer is 10.

Here is another example that involves fractions.

Evaluate the expression

for and .First, substitute

in for the letter and 9 in for the letter in the expression.

Now, simplify the expression using the order of operations. You will need to multiply each part of the expression first.

Remember, to multiply a whole number times a fraction, you can first turn the whole number into a fraction by writing it over 1. Then, multiply the numerators and multiply the denominators. Finally, simplify the fraction.

Next, continue to simplify the expression using the order of operations by adding the two terms.

The answer is 33.

### Guided Practice

Evaluate the expression

for and .First, substitute

in for the letter and in for the letter in the expression.

Now, simplify the expression using the order of operations. You will need to multiply each part of the expression first.

Remember, to multiply fractions you should multiply the numerators and multiply the denominators. Then, simplify the fraction.

Next, continue to simplify the expression using the order of operations by adding the two terms.

Remember, to add fractions you need a common denominator. Here, you already have a common denominator of 3. So, add the numerators of your fractions and keep the common denominator as your denominator.

The answer is

.### Examples

#### Example 1

Evaluate the expression

when is 9 and is 8.First, substitute 9 in for the letter

and 8 in for the letter .

Now, simplify the expression using the order of operations. You will need to multiply first and then add.

The answer is 79.

#### Example 2

Evaluate the expression

when is 2, is 5, and is 7.First, substitute 2 in for the letter , 5 in for the letter , and 7 in for the letter

.

Now, simplify the expression using the order of operations. You will need to multiply each part of the expression first and then add.

The answer is 24.

#### Example 3

Evaluate the expression

when is and is 3.First, substitute

in for the letter and 3 in for the letter in the expression.

Now, simplify the expression using the order of operations. You will need to multiply the first part of the expression first.

Remember, to multiply a whole number and a fraction, you can first turn the whole number into a fraction by writing it over 1. Then, multiply the numerators and multiply the denominators.

Next, continue to simplify the expression using the order of operations by adding the two terms.

Remember, to add fractions you need a common denominator. Here, you already have a common denominator of 4. So, add the numerators of your fractions and keep the common denominator as your denominator. Then, simplify.

The answer is 1.

### Follow Up

Remember Lisa and the new pair of jeans she wants to buy? Her sister Theresa will loan her the money to buy them, but she will need to pay her sister back plus interest. Her sister will use the following expression to calculate how much interest Lisa owes her:

In this expression,

represents the cost of the jeans and represents the number of months before Lisa pays Theresa back.Lisa wants to figure out how much interest she will owe Theresa if the jeans cost $60 and she pays Theresa back in 3 months.

First, Lisa should substitute 60 in for the letter and 3 in for the letter

in the expression.

Now, simplify the expression using the order of operations. You will need to multiply

by 60 and then multiply that result by 3.Remember, to multiply a whole number and a fraction, you can first turn the whole number into a fraction by writing it over 1. Then, multiply the numerators and multiply the denominators. Finally, simplify the fraction.

The answer is that Lisa will owe Theresa $18 in interest if she waits 3 months to pay Theresa back. This means in 3 months she will owe her sister a total of for the jeans and the interest!

### Explore More

Evaluate each expression if

and .1.

2.

3.

4.

5.

Evaluate each expression if and

.6.

7.

8.

9.

10.

Evaluate each expression if

and .11.

12.

13.

14.

15. Evaluate

if is 3 and is 4.16. Evaluate

if is 5, is 4 and is 3.