Why Word Problems Matter
Algebra in the Real World
Word problems show you how algebra is used in everyday life - from calculating costs to figuring out distances, ages, and more!
The 4-Step Problem Solving Strategy
1
READ: Read the problem carefully. What information is given? What are you asked to find?
2
PLAN: Define your variable. What will x (or another letter) represent? Write an equation.
3
SOLVE: Use inverse operations to solve your equation.
4
CHECK: Does your answer make sense? Substitute back into the original problem to verify.
Common Word Problem Types
Types You'll See:
- Addition/Sum: "combined," "total," "in all," "together"
- Subtraction/Difference: "less than," "fewer," "remaining," "left over"
- Multiplication/Product: "times," "per," "each," "groups of"
- Division/Quotient: "divided equally," "split," "shared," "per person"
Pro Tip: Underline the key information and circle what you need to find. This helps you focus on what's important!
Worked Examples
Let's work through different types of word problems step by step.
Example 1: Addition Problem
Maria has some stickers. Her friend gives her 15 more stickers. Now she has 42 stickers in total. How many stickers did Maria start with?
1
READ: Maria gets 15 stickers. Total is now 42. Find: starting amount.
2
PLAN: Let x = stickers Maria started with.
x + 15 = 42
3
SOLVE: Subtract 15 from both sides.
x + 15 - 15 = 42 - 15
x = 27
4
CHECK: 27 + 15 = 42. Yes!
Maria started with 27 stickers.
Example 2: Subtraction Problem
After spending $18 on lunch, Jake has $47 left. How much money did Jake have before lunch?
1
READ: Jake spent $18. He has $47 left. Find: starting amount.
2
PLAN: Let x = money Jake started with.
x - 18 = 47
3
SOLVE: Add 18 to both sides.
x - 18 + 18 = 47 + 18
x = 65
4
CHECK: 65 - 18 = 47. Yes!
Jake had $65 before lunch.
Example 3: Multiplication Problem
A movie ticket costs $12. Write an expression for the total cost of n tickets. Then find how many tickets you can buy with $84.
1
READ: Each ticket = $12. Total = $84. Find: number of tickets.
2
PLAN: Cost of n tickets = 12n. Set up equation:
12n = 84
3
SOLVE: Divide both sides by 12.
12n / 12 = 84 / 12
n = 7
4
CHECK: 12 x 7 = 84. Yes!
You can buy 7 tickets with $84.
Example 4: Division Problem
A pizza is cut into equal slices. If each person gets 3 slices and there are 8 people, how many slices is the pizza cut into?
1
READ: 8 people, 3 slices each. Find: total slices.
2
PLAN: Let s = total slices. Each person gets s / 8 slices.
s / 8 = 3
3
SOLVE: Multiply both sides by 8.
(s / 8) x 8 = 3 x 8
s = 24
4
CHECK: 24 / 8 = 3 slices per person. Yes!
The pizza is cut into 24 slices.
Example 5: Age Problem
Tom is 5 years older than his sister. Tom is 14 years old. How old is his sister?
1
READ: Tom is 5 years older than sister. Tom is 14. Find: sister's age.
2
PLAN: Let s = sister's age. Tom's age = sister's age + 5.
s + 5 = 14
3
SOLVE: Subtract 5 from both sides.
s + 5 - 5 = 14 - 5
s = 9
4
CHECK: 9 + 5 = 14 (Tom's age). Yes!
Tom's sister is 9 years old.
Practice Problems
Solve each word problem. Use the 4-step strategy!
Problem 1: Money
Emma saved some money. She spent $23 on a book and has $52 left. How much money did Emma start with?
Problem 2: Shopping
Notebooks cost $4 each. How many notebooks can you buy with $36?
Problem 3: Distance
After running 7 miles, a runner has completed 12 miles total. How far had the runner already gone?
Problem 4: Sharing
A group of friends shares the cost of a $48 gift equally. Each person pays $8. How many friends are in the group?
Problem 5: Age
Marcus is 3 years younger than his brother. If Marcus is 11 years old, how old is his brother?
Problem 6: Perimeter
A square has a perimeter of 52 cm. What is the length of one side? (Hint: Perimeter = 4 x side)
Problem 7: Temperature
The temperature rose by 12 degrees and is now 68 degrees. What was the starting temperature?
Problem 8: Earnings
Sarah earns $15 per hour babysitting. She earned $90. How many hours did she work?
Next Steps
Key Takeaways:
- Use the 4-step strategy: READ, PLAN, SOLVE, CHECK
- Define your variable clearly - what does it represent?
- Look for key words that indicate which operation to use
- Always check your answer in the context of the problem
- Ask: "Does this answer make sense?"
Practice Makes Perfect! The more word problems you solve, the better you'll become at identifying patterns and setting up equations quickly.
Watch Out: Don't just grab numbers from the problem and combine them randomly. Take time to understand what the problem is really asking!