Money and Pricing Problems
Learn to solve real-world word problems involving money, prices, discounts, and making change.
Definition
- Calculate totals: Add up the cost of multiple items
- Find change: Subtract the purchase amount from the payment
- Apply discounts: Calculate sale prices using percentages
- Determine unit prices: Find the cost per single item or unit
Try it now
Worked Examples
Emma buys 3 notebooks at 4.50 dollars each and 2 pens at 1.75 dollars each. What is her total cost?
Calculate the cost of notebooks
dollars → 13.50 dollars for notebooks
Calculate the cost of pens
dollars → 3.50 dollars for pens
Add both amounts
dollars → Total: 17.00 dollars
Answer: Emma's total cost is 17.00 dollars.
Common Mistakes
Forgetting to multiply quantity times price
Why it's wrong: When buying multiple items, students sometimes just add the price once instead of multiplying.
Correct: If you buy 4 items at 3 dollars each, the cost is dollars, not just 3 dollars.
Subtracting discount percentage from price instead of calculating the actual discount
Why it's wrong: A 20% discount on 50 dollars is not 50 - 20 = 30 dollars.
Correct: First calculate: dollars discount. Then: dollars.
Confusing which number to divide when finding unit price
Why it's wrong: To find price per item, some students divide items by price instead of price by items.
Correct: Unit price = Total price divided by number of items. For 6 dollars for 3 items: dollars per item.
Adding tax before calculating discounts
Why it's wrong: Tax should be calculated on the final price after any discounts are applied.
Correct: First apply the discount, then calculate tax on the discounted price.
Interactive Visual
Ratio Tape Diagram
Adjust the ratio parts using + and - buttons.
Pie Chart
Interactive Sandbox
Expression Calculator
Try these:
History
No calculations yet
Practice Problems
15 problemsSarah buys 4 apples at 0.75 dollars each. What is the total cost?
Why It Matters
- Shopping: Calculate if you have enough money, find the best deals
- Budgeting: Plan your spending for allowance, events, or trips
- Jobs: Count earnings, calculate tips, manage a cash register
- Comparison shopping: Determine which size or brand is the better value
- Saving goals: Figure out how long it takes to save for something you want
Real World Applications
Shopping with a Budget
When shopping with limited money, you need to track your running total to stay within budget.
Example:
You have 25 dollars. A shirt costs 12.99 dollars and socks cost 5.49 dollars. Your total is dollars, leaving you dollars.
You have 40 dollars to spend at the bookstore. You want to buy a book for 14.95 dollars and a journal for 8.50 dollars.
How much money will you have left?
Step 1: Write the mathematical expression
Calculate: 40 - (14.95 + 8.50)
Comparing Store Prices
Smart shoppers compare unit prices to find the best deal, especially when packages come in different sizes.
Example:
Store A sells 6 apples for 3.00 dollars (0.50 dollars each). Store B sells 8 apples for 3.60 dollars (0.45 dollars each). Store B has the better price per apple.
A 500ml bottle of shampoo costs 4.50 dollars. A 750ml bottle costs 6.00 dollars.
Which bottle has the better price per ml?
Step 1: Write the mathematical expression
Compare unit prices: 4.50/500 vs 6.00/750
Restaurant Bills and Tips
When dining out, you need to calculate tips based on the bill amount and sometimes split costs with friends.
Example:
A meal costs 32 dollars. A 15% tip is dollars. Total with tip: dollars.
Your dinner bill is 45 dollars. You want to leave a 20% tip.
What is the total amount you will pay?
Step 1: Write the mathematical expression
Calculate: 45 + (45 x 0.20)
Key Takeaways
- 1Read money problems carefully to identify what you need to find (total, change, discount, unit price)
- 2Total cost = quantity multiplied by price per item, then add all items together
- 3Change = payment amount minus purchase amount
- 4Discount amount = original price multiplied by discount percentage as a decimal
- 5Sale price = original price minus discount amount (or original price multiplied by remaining percentage)
- 6Unit price = total price divided by number of items (useful for comparing values)
- 7Always check your answer makes sense - change should be less than payment, sales price should be less than original
Frequently Asked Questions
Glossary
- Unit price
- The cost of one item or one unit of measurement (e.g., price per ounce or per item)
- Discount
- A reduction from the original price, often expressed as a percentage
- Sale price
- The reduced price after a discount is applied
- Subtotal
- The sum of all items before tax or additional fees are added
- Sales tax
- A percentage added to purchases that goes to the government
- Change
- The money returned when you pay more than the exact purchase amount
Formula Card
Total Cost
Multiply the number of items by the price of each item
Change
Subtract what you owe from what you paid
Discount Amount
Convert percentage to decimal and multiply
Sale Price
Subtract the discount from the original price
Unit Price
Divide total cost by quantity to compare values