FF.3 Solve word problems involving profit
What is profit?
Profit is the money a person or business has left after paying all the costs of making or buying a product. It is the difference between the money earned from selling an item and the money spent to get or make that item. When you sell something for more than it cost you, you make a profit.
- A store buys a toy for $8 and sells it for $12. The profit is $12 − $8 = $4.
- Maya makes bracelets for $3 each and sells them for $7 each. Her profit on one bracelet is $7 − $3 = $4.
- A bakery sells a cake for $25. The ingredients and labor cost $18. The profit is $25 − $18 = $7.
Profit is always a positive number when money is earned. If the selling price is less than the cost, the result is a loss, not a profit. In fourth grade, we focus on situations where a profit is made.
Understanding cost and selling price
Cost is the amount of money spent to buy or make a product. It includes the price paid to a supplier, the cost of materials, and sometimes the cost of labor. Selling price is the amount of money a customer pays to buy the product. Profit is found by subtracting the cost from the selling price.
- Cost = $15, Selling price = $22 → Profit = $22 − $15 = $7.
- Cost = $4.50, Selling price = $6.00 → Profit = $6.00 − $4.50 = $1.50.
- A shop pays $30 for a backpack and sells it for $45. The profit is $15.
Always label your numbers with the dollar sign ($) and use decimal points correctly. Line up the decimal points when subtracting to avoid mistakes.
The profit formula
The relationship between profit, cost, and selling price can be written as a formula:
Profit = Selling Price − Cost
This formula can be rearranged to find the selling price or the cost when the other two values are known.
- If selling price = $20 and cost = $12, then profit = $20 − $12 = $8.
- If profit = $9 and cost = $11, then selling price = $9 + $11 = $20.
- If profit = $6 and selling price = $18, then cost = $18 − $6 = $12.
Memorize the three forms of the formula:
Profit = Selling Price − Cost
Selling Price = Profit + Cost
Cost = Selling Price − Profit
Finding profit when cost and selling price are known
When you know both the cost and the selling price, you can find the profit by subtracting the cost from the selling price. This is the most common type of profit problem.
- A pencil costs the store $0.60 and sells for $1.00. Profit = $1.00 − $0.60 = $0.40.
- A book costs $12.75 and sells for $18.50. Profit = $18.50 − $12.75 = $5.75.
- A video game costs $45 and sells for $60. Profit = $60 − $45 = $15.
When subtracting money, write the numbers vertically and align the decimal points. Borrow when needed, just as with whole numbers.
Finding the selling price when cost and profit are known
If you know the cost of an item and the profit you want to make, you can find the selling price by adding the profit to the cost. This helps store owners decide how much to charge.
- Cost = $14, Profit = $6 → Selling price = $14 + $6 = $20.
- Cost = $3.25, Profit = $2.50 → Selling price = $3.25 + $2.50 = $5.75.
- A baker spends $9 on ingredients and wants a profit of $11. Selling price = $9 + $11 = $20.
When adding money, keep the decimal points lined up. Add the cents first, then the dollars. Regroup if the cents total 100 or more.
Finding the cost when selling price and profit are known
Sometimes you know the selling price and the profit, but you need to find the original cost. In this case, subtract the profit from the selling price.
- Selling price = $25, Profit = $8 → Cost = $25 − $8 = $17.
- Selling price = $10.50, Profit = $3.25 → Cost = $10.50 − $3.25 = $7.25.
- A shop sells a lamp for $40 and makes a profit of $13. The cost was $40 − $13 = $27.
Check your answer by adding the cost and profit together. The sum should equal the selling price.
Profit word problems with multiple items
Many real-world problems involve selling more than one item. To find the total profit, first find the profit for one item, then multiply by the number of items sold. You may also need to find the total cost or total selling price first.
- A student sells 5 cupcakes for $2 each. Each cupcake costs $1 to make. Profit per cupcake = $2 − $1 = $1. Total profit = 5 × $1 = $5.
- A store buys 10 hats for $8 each and sells them for $12 each. Profit per hat = $4. Total profit = 10 × $4 = $40.
- A class sells 25 T-shirts for $15 each. The T-shirts cost $9 each. Profit per shirt = $6. Total profit = 25 × $6 = $150.
Read carefully to see if the problem asks for profit per item or total profit. Sometimes you must find the total cost and total selling price first, then subtract.
Using a table to organize profit problems
A table can help you keep track of cost, selling price, and profit when there are several items. It makes it easier to see which numbers you have and which one you need to find.
| Item | Cost | Selling Price | Profit |
|---|---|---|---|
| Notebook | $2 | $5 | $3 |
| Pen | $1 | $2 | $1 |
| Eraser | $0.50 | $1.25 | $0.75 |
When making a table, label each column clearly. Fill in the numbers you know. Then use the profit formula to find the missing numbers.
Choosing the correct operation
Profit problems require you to decide whether to add or subtract. Use this guide:
• To find profit: subtract cost from selling price.
• To find selling price: add profit to cost.
• To find cost: subtract profit from selling price.
- Cost = $7, Selling price = $13 → Profit = $13 − $7 = $6.
- Cost = $7, Profit = $6 → Selling price = $7 + $6 = $13.
- Selling price = $13, Profit = $6 → Cost = $13 − $6 = $7.
Always ask yourself: “What do I already know?” and “What am I trying to find?” Then choose the matching formula.
Checking your work
After solving a profit problem, check your answer by substituting it back into the formula. If the numbers work, your answer is correct.
- You find profit = $5. Check: Cost $8 + Profit $5 = Selling price $13. Matches.
- You find cost = $12. Check: Selling price $20 − Profit $8 = Cost $12. Matches.
- You find selling price = $25. Check: Cost $17 + Profit $8 = $25. Matches.
Checking your work helps you catch small mistakes, especially when working with decimals or large numbers.
Real-world profit situations
Profit is used in many everyday situations, such as running a lemonade stand, selling handmade crafts, or managing a school store. Understanding profit helps people make smart business decisions.
- A lemonade stand spends $6 on lemons, sugar, and cups. It sells lemonade for $15. Profit = $15 − $6 = $9.
- A student buys a pack of 10 stickers for $3 and sells each sticker for $0.50. Total selling price = 10 × $0.50 = $5. Profit = $5 − $3 = $2.
- A family buys a used bike for $40, repairs it for $15, and sells it for $70. Total cost = $40 + $15 = $55. Profit = $70 − $55 = $15.
In some problems, the cost includes more than one expense. Add all costs together before subtracting from the selling price.
Profit and loss
When the selling price is greater than the cost, there is a profit. When the selling price is less than the cost, there is a loss. A loss is the opposite of a profit. In fourth grade, most problems focus on profit, but it is important to know the difference.
- Cost = $10, Selling price = $14 → Profit = $4.
- Cost = $10, Selling price = $7 → Loss = $3.
- Cost = $25, Selling price = $25 → No profit, no loss (breaks even).
If the selling price is less than the cost, subtract the selling price from the cost to find the loss. The formula is: Loss = Cost − Selling Price.
Large numbers and money
Profit problems can involve larger amounts of money. When numbers have four or more digits, use commas to separate groups of three digits. Always keep the decimal point in the correct place for cents.
- A store buys 100 tablets for $12,500 and sells them for $18,000. Profit = $18,000 − $12,500 = $5,500.
- A company spends $1,250,000 on materials and earns $1,600,000 in sales. Profit = $1,600,000 − $1,250,000 = $350,000.
- A fundraiser collects $2,475 and spends $1,890. Profit = $2,475 − $1,890 = $585.
When writing large numbers, place commas every three digits from the right. For example: 12,500; 1,250,000. This makes the number easier to read.
Common Core alignment: CCSS.MATH.CONTENT.4.OA.A.3 – Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies.
Notes for teachers
This resource is designed to provide clear explanations, examples, and practice for learners of different needs and levels of support. It may be used for whole-class instruction, guided practice, independent learning, review, homework, or additional reinforcement at home.