Page 147 - MAT KS3 Y8 Cambridge CheckPoint

14.3 Solving problems

14.3 Solving problems

If two values are in direct proportion, when one increases or decreases then so does the other,
in the same ratio.
For example, tickets for a concert cost $25 each. Concert
Two tickets cost twice as much: 2 × 25 = $50 tickets
Three tickets cost three times as much: 3 × 25 = $75 $25 each
Ten tickets cost ten times as much: 10 × 25 = $250, etc. Starts 7 30 pm
As the number of tickets increases, so does the total cost, in the same ratio.

You can use the unitary method to solve ratio and proportion problems. The unitary method only works
when the values are in direct proportion. When you use the unitary method you need to find the value
of one part (unit) first.

Worked example 14.3
a Eight folders cost $16. Work out the cost of 5 folders mentally.
b A fruit drink contains orange juice and mango juice in the ratio 2 : 3.
There are 500 ml of orange juice in the drink.
i How much mango juice is there in the drink?
ii How much drink is there altogether?

a 1 folder costs 16 ÷ 8 = $2 In your head, use division to work out the cost of 1 folder
(1 unit) first.
5 folders costs 5 × 2 = $10 In your head, use multiplication to work out the cost of 5
folders.
b i 1 part is worth 500 ÷ 2 = 250 ml 2 parts of the drink are orange juice, so use division to work
out the number of millilitres in 1 part (1 unit) first.
mango juice: 3 × 250 = 750 ml 3 parts of the drink is mango juice, so use multiplication to
work out the number of millilitres in 3 parts.
ii total: 500 + 750 = 1250 ml Add together the number of millilitres of orange and mango juice.
= 1.25 litres Change your answer into litres.

✦ Exercise 14.3

1 Four pens cost $2. Mentally, work out the cost of:
a 1 pen b 3 pens c 10 pens.

2 The cost of two cups of coffee is $3. Mentally, work out the cost of:
a 1 cup of coffee b 5 cups of coffee c 7 cups of coffee.
3 A cleaner is paid $72 for 8 hours’ work.
Mentally, work out how much the cleaner is paid for working 3 hours.
4 Look at the ingredients for honey biscuits.
Mentally, work out how much of each ingredient Honey biscuits (makes 25)
is needed to make: 50 g butter 75 g plain flour
a 100 honey biscuits 75 g icing sugar 100 ml honey
b 40 honey biscuits.

14 Ratio and proportion 145