Word Problems in Algebra – Real-World Applications

Basic Algebra in Full | Lesson 10

🧠 What You’ll Learn

In this lesson, you’ll learn how to convert real-world situations and word problems into algebraic equations using logical reasoning, mathematical language, and structured problem-solving techniques.

You’ll learn how to:

• Understand what algebra word problems and real-world applications are
• Recognize common mathematical language used in word problems and translate it correctly into algebra
• Interpret keywords such as sum, difference, product, increase, double, and per
• Identify unknown quantities and represent them using suitable variables
• Decide which variable to use when multiple unknowns appear in a problem
• Express dependent quantities in terms of a single variable
• Translate complex word problems into algebra one step at a time
• Break long statements into smaller parts to avoid common modelling mistakes
• Apply real-world knowledge and common sense when interpreting mathematical situations
• Recognize when background knowledge is needed to understand a problem correctly
• Work confidently with units and convert quantities into matching units before calculating
• Understand why unit consistency is essential in mathematical problem solving
• Combine multiple algebra skills from across the Basic Algebra in Full series to solve practical problems
• Create and solve equations from shopping, pricing, age, quantity, and measurement scenarios
• Model relationships involving fractions, capacities, and proportional quantities
• Solve problems involving consecutive numbers and numerical patterns
• Build algebraic models from multi-step real-life situations involving several connected pieces of information
• Develop reasoning skills that allow you to approach unfamiliar word problems confidently
• Learn how mathematical investigation, logic, and structured thinking work together to solve real-world problems

By the end, you’ll be able to translate a wide range of word problems into algebraic equations, solve them accurately, and understand the reasoning that connects mathematics to everyday situations.

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🧩Practice Exercises

These exercises help you build from foundation to advanced understanding.

You can:

  • Start at your level
  • Or work through all levels step by step

✍️ Attempt exercises before checking answers.

🎯 Levels

Each level matches a stage of learning and shows
what you should be able to understand and solve at that point.

🟢 Foundation → You’re learning this topic for the first time
🟠 Developing → You understand the basics and are building on them
⚪ Confident → You’re ready for deeper, multi-step problems
⚫ Advanced → You want to challenge your understanding further

📘 Not sure where you fit? → View Level Guide

💡 Each set of exercises is designed to match what students at that stage are typically expected to handle.

Start with your level, then try the next one when you feel ready.

  1. A fruit seller sells mangoes for \$3 each. A customer spends \$36 on mangoes. How many mangoes did the customer buy?
  2. A number is multiplied by $4$ and then increased by $7$. The result is $31$. Find the number.
  3. A school bus carries some pupils. After $12$ pupils get off, there are $25$ pupils left. How many pupils were on the bus originally?
  4. Four reward tokens can be exchanged for one free snack. A student collects $48$ tokens. How many free snacks can be claimed?
  5. A bottle is $\frac{1}{3}$ full. If $20$ litres are added, it becomes full. What is the capacity of the bottle?
Show Answers
  1. $12$
  2. $6$
  3. $37$
  4. $12$
  5. $30\text{ litres}$

  1. Sarah is $5$ years older than David. Their ages add up to $35$. Find their ages.
  2. Three consecutive whole numbers have a sum of $72$. Find the numbers.
  3. A teacher buys $25$ notebooks at $£4$ each and some pens costing $£2$ each. She spends $£130$ altogether. How many pens did she buy?
  4. A water tank is $\frac{1}{4}$ full. After $18$ litres are added, it becomes $\frac{1}{2}$ full. Find the capacity of the tank.
  5. Mark has three times as many stickers as Ben. Together they have $56$ stickers. How many stickers does each have?
Show Answers
  1. $15\text{ years and }20\text{ years}$
  2. $23,\ 24,\ 25$
  3. $15$
  4. $72\text{ litres}$
  5. $14\text{ and }42$

  1. Nadia is $3$ years older than Grace, and Grace is $4$ years older than Amina. Their combined age is $49$ years. Find the age of each girl.
  2. Kate has four times as many marbles as Mary. If Kate gives $15$ marbles to Mary, they will have the same number. How many marbles does each currently have?
  3. A man earns $£400$ more each year than the previous year. Over four years he receives a total of $£12,400$. How much did he earn in the first year?
  4. A number multiplied by $5$ and then reduced by $8$ gives the same result as doubling the number and adding $19$. Find the number.
  5. A tank is $\frac{2}{5}$ full. After $24$ litres are added, it becomes $\frac{4}{5}$ full. Find the capacity of the tank.
Show Answers
  1. $14,\ 18,\ 17$
  2. $10\text{ and }40$
  3. $2,500$
  4. $9$
  5. $60\text{ litres}$

  1. A bus starts a journey with $64$ passengers. At the first stop, $x$ passengers get off and $6$ get on. At the next stop, one-third of the passengers then on the bus get off and $4$ get on. There are now $30$ passengers. Find $x$.
  2. A mother is $24$ years older than her daughter. Ten years ago, the mother was three times as old as the daughter was then. Find their current ages.
  3. Mr Kumar leaves his savings equally among three sons and four daughters. Each son receives twice as much as each daughter. The remaining $₹12,000$ goes to his wife and represents one-quarter of the total money. How much does each son receive?
  4. Mark has five times as many books as John. If Mark gives $16$ books to John, they will then have the same number of books. How many books did each have originally?
  5. A woman buys apples and tomatoes from a vendor. An apple costs ₦500 and a tomato costs ₦200. She buys twice as many tomatoes as apples and pays the vendor ₦9,800. The change she receives is equal to four times the product of ₦20 and the number of apples she bought. How many apples did she buy? (Note: change means balance or cash back or left-over money)
Show Answers
  1. $29$
  2. $26\text{ years and }50\text{ years}$
  3. $₹8,000$
  4. $20\text{ books and }100\text{ books}$
  5. $10$

🔁 Continue Learning

⏮️ Back to Basic Algebra in Full
⏭️ Next Lesson → Intermediate Algebra in Full series, Lesson 1

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