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. x. 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 x years old. George is 4 years older than Fred. Harry is twice as old as George. Write expressions, in terms of x for their ages.
Fred
| |
George | |
Harry | 2(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, C, of a mobile phone bill is the cost of text messages, t, and the cost of calling, m. Texts are 5p each, and each minute of a call is 10p. Write a formula for the cost, C, of the mobile phone bill.
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 for delivering pizzas, through a delivery app. They charge a standard fee of £1.50 and an additional 80p for each mile, m, travelled. Write a formula for C and work out the charge for a 5 mile delivery.
C=0.8m+1.5
Note: Remember to convert to the same units if necessary, in this case 80p has been converted to £0.8.
Now use the formula by substituting m=5 to calculate the cost.
C=0.8×5+1.5=5.5
The total cost is £5.50