S4 Mathematics - Term 1

Topic 2: Equations and Inequalities

Lesson 7: Complex Word Problems

Duration: 40 minutes

Learning Outcomes

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

• Solve word problems involving consecutive integers
• Apply equations to geometry problems
• Handle problems requiring multiple steps

Today's Problem Types

1. Consecutive integers - numbers in sequence
2. Geometry problems - angles, triangles
3. Multi-condition problems - more complex setups

Remember: Read carefully - every word matters!

Consecutive Integers

Example 1: Regular Consecutive

"The sum of three consecutive integers is 72. Find them."

• Let first = n
• Second = n + 1
• Third = n + 2
• Equation: n + (n + 1) + (n + 2) = 72
• Simplify: 3n + 3 = 72
• Solve: n = 23
• Integers: 23, 24, 25

Example 2: Even Consecutive

"The sum of three consecutive even numbers is 48."

• Let first = n
• Second = n + 2
• Third = n + 4
• Equation: n + (n + 2) + (n + 4) = 48
• Simplify: 3n + 6 = 48
• Solve: n = 14
• Numbers: 14, 16, 18

Pair Practice

1. "The sum of two consecutive odd numbers is 36. Find them."

2. "Three consecutive integers: the largest is twice the smallest minus 6. Find them."

Answers

1. n + (n + 2) = 36
   2n + 2 = 36
   n = 17
   Numbers: 17 and 19

2. Let integers be n, n+1, n+2
   Largest = n + 2
   n + 2 = 2n - 6
   8 = n
   Integers: 8, 9, 10

Triangle Angles

Remember: Angles in a triangle sum to 180 degrees

"The second angle is twice the first. The third is 30 degrees more than the first. Find all angles."

Triangle Solution

• First angle = x
• Second = 2x
• Third = x + 30

x + 2x + (x + 30) = 180
4x + 30 = 180
4x = 150
x = 37.5

Angles: 37.5 degrees, 75 degrees, 67.5 degrees

Supplementary Angles

Supplementary angles sum to 180 degrees

"Two supplementary angles differ by 40 degrees."

• Smaller = x
• Larger = x + 40
• x + (x + 40) = 180
• 2x = 140
• x = 70

Angles: 70 degrees and 110 degrees

Complementary Angles

Complementary angles sum to 90 degrees

"Two complementary angles: one is 20 degrees more than the other."

• x + (x + 20) = 90
• 2x = 70
• x = 35

Angles: 35 degrees and 55 degrees

Individual Practice

1. "Angles in a triangle are in ratio 2:3:4. Find each angle."

2. "The length of a rectangle is 5 cm more than the width. Perimeter is 42 cm. Find the area."

Answers

1. Let angles be 2k, 3k, 4k
   2k + 3k + 4k = 180
   9k = 180
   k = 20
   Angles: 40 degrees, 60 degrees, 80 degrees

2. Width = w, Length = w + 5
   2(w + 5) + 2w = 42
   4w + 10 = 42, w = 8
   Width: 8 cm, Length: 13 cm
   Area: 8 times 13 = 104 cm squared

Problem-Solving Strategies

Problem Type	Key Relationship
Consecutive (regular)	n, n+1, n+2
Consecutive (even/odd)	n, n+2, n+4
Triangle	Angles sum to 180 degrees
Supplementary	Sum to 180 degrees
Complementary	Sum to 90 degrees
Ratio ac	Use ak, bk, ck

Exit Problems

1. "The sum of two consecutive odd numbers is 52. Find them."

2. "Two angles are complementary. One is 20 degrees more than the other."

Answers

1. n + (n + 2) = 52
   2n = 50
   n = 25
   Numbers: 25 and 27

2. x + (x + 20) = 90
   2x = 70
   x = 35
   Angles: 35 degrees and 55 degrees

Homework

1. Sum of four consecutive integers is 86
2. Three consecutive odd numbers sum to 63
3. Complementary angles: one is 4 times the other
4. Triangle angles in ratio 1:2:3
5. Rectangle: length is 8 cm more than width, area is 84 cm squared

Next Lesson

Lesson 8: Equations Review and Assessment

• Review all equation-solving techniques
• Practice mixed problems
• Assessment preparation

Credits

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

Source: National Curriculum Development Centre (NCDC), Uganda