Step 1: Read the problem carefully

Identify what we know and what we need to find.

Step 2: Choose a variable

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

Step 3: Translate key phrases

Convert each verbal phrase into an algebraic term.

Example 1: Simple Expression

Problem: A pen costs TZS x. What is the cost of 5 such pens?

Solution:

• We know: cost of 1 pen = TZS x
• We need: cost of 5 pens
• Operation: multiplication
• Expression: 5x

Example 2: Creating an Equation

Problem: Mwanajuma has TZS 5000. She buys 3 books at TZS y each. After buying, she has TZS 2000 left. Find the cost of each book.

Solution:

• Money spent = 3y
• Money left = 5000 − 3y
• This equals 2000: $5000 - 3y = 2000$

Now solve: $5000 - 2000 = 3y$ $3000 = 3y$ $y = 1000$

Each book costs TZS 1000.

Example 3: Two Unknowns

Problem: In a farm, there are chickens and cows. The total number of animals is 15. The total number of legs is 40. How many chickens are there?

Solution:

• Let: number of chickens = c, number of cows = k
• Equation 1 (total animals): c + k = 15
• Equation 2 (total legs): 2c + 4k = 40

From equation 1: c = 15 − k

Substitute into equation 2: $2(15 - k) + 4k = 40$ $30 - 2k + 4k = 40$ $30 + 2k = 40$ $2k = 10$ $k = 5$

Therefore: c = 15 − 5 = 10

There are 10 chickens.

• Always identify what the variable represents clearly
• Write down what each expression means in words
• Check if your answer makes sense in the original problem
• Look for keywords but also understand the context

• "n more than a number" → x + n
• "twice a number" → 2x
• "half of a number" → x/2
• "the difference between a number and 7" → x − 7
• "a number divided by 4" → x/4
• "the sum of two consecutive numbers" → n + (n + 1)

In Tanzania, algebraic modeling helps with everyday calculations. For example, when a vendor at Buguruni Market buys 10 mangoes at TZS y each and sells them for TZS 5000 total, they can use the equation 10y = 5000 to find that each mango cost TZS 500, then calculate their profit or loss. This skill is essential for small business owners, farmers, and anyone managing money in daily life.