UK Secondary (7-11)

Multi-step word problems (arithmetic operations)

Lesson

The beauty of mathematics is that it helps us solve problems in everyday life. For example, if I wanted to buy a new watch for $\$150$$150 and I knew that I could save $\$50$$50, the I could use my maths knowledge to work out that I could buy my new watch in $3$3 weeks because $150\div50=3$150÷50=3.

As we saw when we looked at worded arithmetic problems, we need to convert the worded problem into an equation, then solve it as a multi-step equation. Sometimes we can solve these kinds of problems as number equations but sometimes it's easier to include algebraic terms.

Handy Hint

Here are some common expressions for each of the four operations. See if you can think of any more to add to the list

- Addition: more than, plus, older, increase, sum, total
- Subtraction: less than, minus, younger, decrease, difference, take away, deduct
- Multiplication: groups of, times, by, product
- Division: split into equal groups, quotient, goes into

Let's look through some examples.

You have $\$7.54$$7.54 in your pocket. You want to buy $5$5 items, that cost $\$0.19$$0.19 each. How much change will you have after your purchase?

Bob is planning on driving $4000$4000 kilometres, traveling with $3$3 friends. The car consumes $5$5 litres of petrol every $100$100 kilometres. Petrol costs $\$1.40$$1.40 per litre. If they split the cost of petrol for the trip evenly, how much will Bob pay for petrol?

a) How many litres of petrol will be used on the trip?

b) How much will it cost to buy $200$200 litres of petrol?

c) How much will Bob pay? Round to the nearest cent if necessary.

Laura is reseeding her lawn with grass seed. Her lawn is $20$20 metres by $16$16 metres. She wants to buy packets of grass seed which state "$1$1 box covers $8$8 square metres of lawn". Each box costs $\$6.00$$6.00. How much will it cost to completely cover her lawn in grass seed?