## Lesson Intro: Expressions with Variables

In this lesson, Juni Mathematics instructor **Kadyn** talks about **variables and variable expressions** - foundational concepts in pre-algebra. Variables are important to know for higher levels of math, and are even used similarly in other subjects like computer science!

Read Kadyn's Intro to Variable Expressions lesson first to understand what variables are and how to use them in expressions. Then, use what you've learned with Kadyn's **word problems** below to translate sentences and real-life problems into expressions with unknown variables. Learn to solve for unknowns, and tackle real-world applications.

Once you've checked your answers, you can also keep practicing using variables with Variable Expressions Drills and Warmup Problems.

## Word Problems

### Problem 1:

**Write out the following mathematical expression in full and then in simplified form:** negative three times the difference of five times x and the absolute value of negative two minus three.

### Problem 2:

Ted is hosting a birthday party. If you take the number of friends he invited and multiply it by 4 and subtract it by 7, you get 53. How many people did Ted invite to his party?

### Problem 3:

Carmen wants to collect stamps and the store charges $3 for a pack of 12 stamps. How many stamps will Carmen have if she spent $36 on stamps? (disregard taxes)

### Problem 4:

Peter wants to build a rectangular fence around his yard. One side of the fence is 3m shorter than 4 times the other side. If the shorter side of the fence is 15m, what is the perimeter of the fence in meters?

### Problem 5:

Elliott and Gretchen are renting their own apartments in the city. Elliott has paid $10,000 in rent so far and Gretchen has paid $8,000. If both of them have been renting their own place for the same number of months and Gretchen’s monthly rate is $1,000, how much is Elliott’s monthly rent?

## Find Solutions Below

## Answer Key

### Problem 1

-3 ⋅ (5x - |-2 -3|) = -3 ⋅ (5x - 5) = -15x + 15

**Full form:** -3 ⋅ (5x - |-2 -3|)

**Simplified form:** -15x + 15

### Problem 2

Ted invited 15 people to his birthday party.

Let the number of people at Ted’s birthday party be n. Then n ⋅ 4 - 7 = 53 → n ⋅ 4 = 60. Then we know that n = 15.

### Problem 3

Carmen has 144 stamps.

Let the number of stamps that Carmen has be s. Since she spent $36 on stamps and each pack of stamps cost $3, she then bought 36 3 = 12 packs. Since each pack comes in with 12 stamps, she has 12 ⋅ 12 = 144 stamps.

### Problem 4

The perimeter of the fence is 144m.

Since the shorter side of the fence is 15m long, the longer side of the fence is 4 ⋅ 15 - 3 = 57m long. Then the perimeter of the fence is 15 + 15 + 57 + 57 = 144m.

### Problem 5

Elliott’s monthly rent is $1,250.

Since Gretchen has paid $8,000 in rent and her monthly rent is $1,000, she has lived at her place for 8,000 1,000 = 8 months. Since Gretchen has lived at her place as long as Elliott has lived at his, we know that Elliott has lived at his place for 8 months as well. Then since Elliott has paid $10,000 in rent, his monthly rate is $10,000 8 = $1,250.

## More Exercises on Variables

We hope you enjoyed Kadyn's Word Problems with Variable Expressions! This lesson falls under our Pre-Algebra A course curriculum.

Continue practicing variable expressions with warmup problems and practice drills below. Or, review key terms and concepts with Kadyn's Intro to Variables lesson.

- Intro to Variable Expressions: Definitions and Approaches
- Warmup Questions with Variable Expressions
- Variable Expressions Drills

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