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Writing formulae and equations from word problems

Writing formulae and equations from word problems

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Simplifying algebraic expressions

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Writing formulae and equations from word problems

Writing formulae and equations from diagrams

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Sequences

Finding the nth term

Solving inequalities

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Iteration - Higher

Simultaneous equations: elimination and substitution

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Algebraic proof - Higher

Composite and inverse functions - Higher

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Types of numbers

Order of operations: BODMAS

Multiplying and dividing by powers of 10

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Prime numbers and prime factorisation

Multiples, factors and prime factors

LCM and HCF

Fractions

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Writing recurring decimals as fractions

Rounding: Integers, decimal places, significant figures

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Error intervals

Upper and lower bounds - Higher

Powers and roots: Square and cube numbers

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Rationalising surds - Higher

Standard form calculations

Explainer Video

Tutor: Meera

Summary

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. xxx. 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 xxx years old. George is 444 years older than Fred. Harry is twice as old as George. Write expressions, in terms of xxx for their ages.


Fred
​xxx​​
George
​x+4x+4x+4​​
Harry
​2(x+4)=2x+82(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, CCC, of a mobile phone bill is the cost of text messages, ttt, and the cost of calling, mmm. Texts are 5p5p5p each, and each minute of a call is 10p10p10p. Write a formula for the cost, CCC, of the mobile phone bill.


C=0.05t+0.1m‾\underline{C= 0.05t+0.1m}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£C for delivering pizzas, through a delivery app. They charge a standard fee of £1.50£1.50£1.50 and an additional 80p80p80p for each mile, m, travelled. Write a formula for CCC and work out the charge for a 555 mile delivery.


​C=0.8m+1.5C=0.8m+1.5C=0.8m+1.5​

Note: Remember to convert to the same units if necessary, in this case 80p80p80p has been converted to £0.8£0.8£0.8.


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

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

​

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


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Simple formulae

Unit 1

Simple formulae

Writing and using formulae

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Writing and using formulae

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Writing formulae and equations from word problems

Unit 3

Writing formulae and equations from word problems

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FAQs - Frequently Asked Questions

How can you check if a formula you created works?

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

How can I create a formula in algebra?

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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