Mathematics, Algebra and Function, Problem Solving

Grade 5- 8

### Objective

Students will learn about solving word problems using simple algebra functions.

### Directions

Many basic word problems can be expressed in an equation format, which makes it easy to understand and solve.

**Using Algebraic Symbols**

You can use a letter of the alphabet to represent the unknown number in a problem. The equation is written so that the values on the left side of the equal sign equal the values on the right side of the equal sign. Solve the equation so that the unknown value represented by a letter is alone on one side of the equal sign and the value of the unknown is on the other side of the equal sign.

**Sample:** Jennifer has $25.00. She needs $49.00 to buy a new school outfit. How much more money does she need? Write an equation this way: *n>/i> (money needed) + 25 (money she has) = 49 (cost of outfit); Solve the equation by subtracting 25 from each side. Jennifer needs $24.00 more.*

n + 25 = 49

n + 25 - 25 = 49 - 25

n = 24

**Axiom of Equality**

The axioms of equality were used to help solve the basic equation above. Any value added, subtracted, multiplied, or divided to one side of the equal sign must be added, subtracted, multiplied, or divided respectively to the other side.

**Sample:** A group of 5 girls decided to split evenly the $18.75 cost of a CD album by their favorite group. How much money did each girl spend? Write an equation. Solve for n (the amount each girl spent) by dividing each side of the equation by 5. Each girl spent $3.75.

5n = $18.75

5n / 5 = $18.75 / 5

n = $3.75

**Working with Two Unknown Quantities**

You can use the same letter with an added or subtracted amount to represent two unknown quantities. Simplify and combine terms whenever possible.

**Sample:** Sammy's mother is 2 years more than 3 times as old as Sammy. Their combined age is 42. How old are Sammy's mother and Sammy? Write an equation where *n* equals Sammy's age. Let 3n + 2 = Sammy's mother's age. Since the total of their ages equals 42, then n + 3n + 2 = 42; Then combine the terms: 4n + 2 = 42; Use the axioms of equality by subtracting 2 and then dividing by 4. Sammy is 10 years old. His mother is 32 years old.

4n + 2 = 42

4n + 2 - 2 = 42 - 2

4n = 40

4n / 4 = 40 / 4

n = 10

### Resources

- copies of the activity sheets (see the link below)