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Writing formulae and equations from word problems

Writing formulae and equations from word problems

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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. 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.


Fred
xx​​
George
x+4x+4​​
Harry
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.


C=0.8m+1.5C=0.8m+1.5

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}


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FAQs - Frequently Asked Questions

How can you check if a formula you created works?

How can I create a formula in algebra?

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