S4 Mathematics - Term 1

Topic 2: Equations and Inequalities

Lesson 6: Word Problems with Equations

Duration: 40 minutes

Learning Outcomes

By the end of this lesson, you should be able to:

• Translate word problems into algebraic equations
• Solve equations arising from real-life contexts
• Interpret solutions and check for reasonableness

The Challenge

"I think of a number, double it, and add 5. The result is 17. What is my number?"

Can you solve this in your head?

Systematic Approach

Let the number be x

"Double it": 2x

"Add 5": 2x + 5

"Result is 17": 2x + 5 = 17

Solve: 2x = 12, x = 6

Word Problem Strategy

Example 1: Number Problem

"Three times a number minus 7 equals 14. Find the number."

• Let the number be n
• Three times: 3n
• Minus 7: 3n - 7
• Equals 14: 3n - 7 = 14
• Solve: 3n = 21, n = 7
• Check: 3(7) - 7 = 21 - 7 = 14 check!

Example 2: Age Problem

"Amina is 5 years older than Kwame. The sum of their ages is 31. Find their ages."

• Let Kwame's age = x
• Amina's age = x + 5
• Sum: x + (x + 5) = 31
• Simplify: 2x + 5 = 31
• Solve: 2x = 26, x = 13
• Kwame: 13, Amina: 18
• Check: 13 + 18 = 31 check!

Example 3: Perimeter

"A rectangle's length is 3 cm more than its width. The perimeter is 26 cm. Find the dimensions."

• Let width = w, length = w + 3
• Perimeter: 2(w + 3) + 2w = 26
• Expand: 2w + 6 + 2w = 26
• Simplify: 4w + 6 = 26
• Solve: 4w = 20, w = 5
• Width: 5 cm, Length: 8 cm

Example 4: Money Problem

"A pen costs 500 shillings more than a pencil. Three pens and two pencils cost 4,600 shillings."

• Let pencil = p, pen = p + 500
• Equation: 3(p + 500) + 2p = 4600
• Expand: 3p + 1500 + 2p = 4600
• Simplify: 5p + 1500 = 4600
• Solve: 5p = 3100, p = 620
• Pencil: 620/=, Pen: 1,120/=

Pair Practice

1. "I think of a number, multiply by 4, and subtract 3. The result is 25. What is my number?"

2. "The sum of two consecutive numbers is 47. Find the numbers."

Answers

1. Let n be the number
   4n - 3 = 25
   4n = 28
   n = 7

2. Let the numbers be n and n + 1
   n + (n + 1) = 47
   2n + 1 = 47
   2n = 46
   n = 23, so numbers are 23 and 24

Individual Practice

1. "Mary has 200 shillings more than John. Together they have 1,400 shillings. How much does each have?"

Answer

Let John have j shillings
Mary has j + 200 shillings

j + (j + 200) = 1400
2j + 200 = 1400
2j = 1200
j = 600

John: 600/=, Mary: 800/=

Check: 600 + 800 = 1400 check!

Key Tips

1. Define x clearly - state what it represents
2. Look for key words - sum, difference, times, etc.
3. Translate step by step - don't rush
4. Check in context - does the answer make sense?

Exit Problems

1. "Five times a number decreased by 8 equals 27. Find the number."

2. "A rectangle's length is twice its width. The perimeter is 36 cm. Find the dimensions."

Answers

1. 5n - 8 = 27; 5n = 35; n = 7

2. Let width = w, length = 2w
   2(2w) + 2w = 36
   6w = 36
   w = 6
   Width: 6 cm, Length: 12 cm

Homework

1. "I think of a number, add 9, and multiply by 2. Result is 40."
2. "The sum of two numbers is 45. One is 7 more than the other."
3. "A book costs 3 times as much as a notebook. Together: 2,000/="
4. "Sarah is 8 years older than her sister. Five years ago, Sarah was twice as old."
5. "Rectangle perimeter is 54 cm. Length is 3 cm less than twice the width."

Next Lesson

Lesson 7: More Complex Word Problems

We will tackle:

• Multi-part problems
• Problems with more variables
• Geometric applications

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda