Step 1: Read the problem carefully

Identify what we need to find and what information is given.

Step 2: Choose a variable

Let the unknown quantity be represented by a letter (commonly $x$, $y$, $n$, or any letter).

Step 3: Translate the problem into an equation

Write the mathematical relationship using the variable, numbers, and operations.

Step 4: Check that both sides are equal

Make sure the equation represents the situation correctly.

Example 1: Simple addition equation

Problem: Amina has some oranges. Her mother gives her 5 more oranges. Now she has 12 oranges. How many oranges did Amina have at first?

Solution:

Let $x$ = number of oranges Amina had at first

Her mother gives her 5 more: $x + 5$

Now she has 12 oranges: $x + 5 = 12$

The algebraic equation is: $x + 5 = 12$

Example 2: Subtraction equation

Problem: Juma spent 250 shillings on a pencil and remained with 1,000 shillings. How much money did Juma have before buying the pencil?

Solution:

Let $y$ = amount of money Juma had before buying the pencil

He spent 250 shillings: $y - 250$

He remained with 1,000 shillings: $y - 250 = 1000$

The algebraic equation is: $y - 250 = 1000$

Example 3: Multiplication equation

Problem: The price of one exercise book is 500 shillings. Fatuma bought several exercise books and paid 4,000 shillings. How many exercise books did Fatuma buy?

Solution:

Let $n$ = number of exercise books

Price of one book × number of books = total price

$500 \times n = 4000$

The algebraic equation is: $500n = 4000$

Example 4: Division equation

Problem: A teacher shared 60 notebooks equally among some students. Each student received 12 notebooks. How many students received notebooks?

Solution:

Let $s$ = number of students

Total notebooks ÷ number of students = notebooks per student

$60 \div s = 12$

The algebraic equation is: $\frac{60}{s} = 12$

Example 5: Two-step equation

Problem: Rehema is 5 years older than Kemi. The sum of their ages is 25 years. Find their ages.

Solution:

Let $x$ = Kemi's age

Rehema is 5 years older: $x + 5$

Sum of their ages: $x + (x + 5) = 25$

The algebraic equation is: $x + x + 5 = 25$

Simplified: $2x + 5 = 25$

Example 6: Equation with variable on both sides

Problem: In a school, the number of boys is 20 more than the number of girls. The total number of students is 350. If $g$ represents the number of girls, write an equation to find $g$.

Solution:

Number of girls = $g$

Number of boys = $g + 20$

Total students = $g + (g + 20) = 350$

The algebraic equation is: $g + g + 20 = 350$

Simplified: $2g + 20 = 350$

Try to write the algebraic equation for each problem. Do not solve yet—just write the equation.

1. Peter has $x$ shillings. His father gives him 200 shillings. Now he has 500 shillings. Equation: $x + 200 = 500$

2. A bus fare to Dodoma is $y$ shillings. Sarah paid 3,000 shillings for 3 bus tickets. Equation: $3y = 3000$

3. A rectangle has width 5 metres and length $l$ metres. Its perimeter is 30 metres. Equation: $2(5 + l) = 30$

4. Twenty children shared some mangoes equally. Each child received 4 mangoes. Equation: $20 \times 4 = m$ or $\frac{m}{20} = 4$

5. The price of 1 kg of rice is $p$ shillings. Maria bought 5 kg and paid 10,000 shillings. Equation: $5p = 10000$

• An equation always has an equal sign (=)
• The variable (letter) represents the unknown quantity
• Both sides of the equation must be equal in value
• To write an equation, translate the words into mathematical symbols
• Choose a clear letter that makes sense (or use any letter like $x$, $y$)
• The equation should represent the exact situation described in the problem

• Forgetting the equal sign: Every equation must have "="
• Using the wrong operation: Carefully read words like "more than" (add) or "less than" (subtract)
• Not including all quantities: Make sure both sides of the equation represent the same total or relationship

In everyday life in Tanzania, writing algebraic equations helps solve practical problems. For example, when running a small kiosk or shop, a vendor can write an equation to calculate profit: if a packet of sugar costs $x$ shillings and is sold for 3,000 shillings with a profit of 500 shillings, the equation $x + 500 = 3000$ or $3000 - x = 500$ can be used to find the cost price. This skill is also useful for budgeting money, calculating market prices, and solving everyday trading problems.