Page 141 - Mathematics Coursebook

14.3 Using direct proportion

14.3 Using direct proportion

Two quantities are in direct proportion when their ratio stays the same as the
quantities increase or decrease.
One packet of rice costs $3.25, so two packets of rice would cost twice as much.
Two packets of rice would cost 2 × $3.25 = $6.50.
Six tickets to a concert cost $120, so three tickets would cost half as much.
!ree tickets would cost $120 ÷ 2 = $60.

Worked example 14.3

a Three books cost $12. Work out the cost of 10 books.
b A recipe uses two eggs to make 12 cupcakes.
How many eggs are needed to make 36 cupcakes?

a $12 ÷ 3 = $4 First of all, work out the cost of one book
by dividing the total cost of the books by 3. This is called the unitary
10 × $4 = $40 Now work out the cost of 10 books by method, because you fi nd
multiplying the cost of one book by 10. the cost of 1 book before
b 36 ÷ 12 = 3 You can see that to make 36 cupcakes you fi nding the cost of 10.
need to multiply the recipe by 3.
2 × 3 = 6 eggs So, multiply the number of eggs by 3.

) Exercise 14.3

1 Tony buys one bag of chips for $1.20. In this type of question, if you can see the
Work out the cost of: connection between the numbers, you don’t need
a two bags of chips b five bags of chips. to use the unitary method.

2 Rob goes to the gym three times a week.
Work out how many times he goes to the gym in: Remember that there are 52 weeks in a year.
a four weeks b one year.
3 Three bananas weigh 375 grams.

Copy and complete the working to find the weight of eight bananas.
1 banana weighs: 375 ÷ 3 =
8 bananas weigh: 8 × =

4 Five apples weigh 320 grams.
Work out the weight of: a one apple b seven apples.

5 Ivan buys four shirts for $37.80.
Work out the cost of nine shirts.
6 A recipe for four people uses 800 g of chicken.
Copy and complete the workings to find the weight of chicken needed for:

a 20 people b 6 people.
a Weight of chicken for 4 people: 800 g
The connection between 4 and 20 is: 20 ÷ 4 =
Weight of chicken for 20 people: 800 g × = g

140 14 Ratio and proportion