Chapter overview



Writing formulae and equations from word problems

Your lesson progress



Writing formulae and equations from word problems

In a nutshell

You should be able to form expressions or formulae from information given in a question. Start by giving the unknown quantities a letter name, e.g. xx. Then use the information in the question to create your expression or formula.

Note: Remember to substitute into the formula to check that is works.


Make an expression

To make an expression, read the information given, give the unknown quantity a letter name and use your knowledge of algebra to write the correct expression.

Example 1

Fred is xx years old. George is 44 years older than Fred. Harry is twice as old as George. Write expressions, in terms of xx for their ages.

2(x+4)=2x+82(x+4) = 2x+8​​

Make a formula

To make a formula, read the information given, give the unknown quantity a letter name and use your knowledge of algebra to give the formula.

Example 2

The total cost, CC, of a mobile phone bill is the cost of text messages, tt, and the cost of calling, mm. Texts are 5p5p each, and each minute of a call is 10p10p. Write a formula for the cost, CC, of the mobile phone bill.

C=0.05t+0.1m\underline{C= 0.05t+0.1m}

Use a formula to calculate the unknown quantity

Create a formula, as above, then substitute in for the variables in the formula to calculate the result.

Example 3

A restaurant charges £C£C for delivering pizzas, through a delivery app. They charge a standard fee of £1.50£1.50 and an additional 80p80p for each mile, m, travelled. Write a formula for CC and work out the charge for a 55 mile delivery.


Note: Remember to convert to the same units if necessary, in this case 80p80p has been converted to £0.8£0.8.

Now use the formula by substituting m=5m=5 to calculate the cost.​

C=0.8×5+1.5=5.5C = 0.8 \times 5 + 1.5 = 5.5

The total cost is £5.50\underline{£5.50}

Want to find out more? Check out these other lessons!

Writing and using formulae

Frequently Asked Questions (FAQ)


  • Question: How can you check if a formula you created works?

    Answer: After creating a formula, you can check it works by substituting values to make sure that the answer is as expected.

  • Question: How can I create a formula in algebra?

    Answer: A formula can be created by analysing a questions, given in context. Letters can be used for the unknown variables to help create the formula.



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