Page 139 - Cambridge+Checkpoint+Mathematics+Coursebook+9

14.2 Solving problems

14.2 Solving problems

You already know that two quantities are in direct proportion when their ratios stay
the same as they increase or decrease. For example, when you buy a bottle of milk, the
more bottles you buy, the more it will cost you.
!e two quantities, number of bottles and total cost, are in direct proportion.

When you own a car, the value of the car decreases each year that you own it.
So, as the number of years increases the value of the car decreases.
!e two quantities, number of years and value of car, are not in direct proportion.

Worked example 14.2

a Are these quantities in direct proportion?
i the cost of fuel and the number of litres bought
ii the age of a house and the value of the house
b 12 sausages have a mass of 1.5 kg.
What is the mass of 16 sausages?
c A 500 g box of cereal costs $3.20. A 200 g box of the same cereal costs $1.30.
Which box is better value for money?
d When Greg went to Spain the exchange rate for dollars to euros was $1 = €0.76.
i Greg changed $200 into euros. How many euros did he get?
ii Greg changed €19 back into dollars. How many dollars did he get?

a i Yes The more litres of fuel you buy, the more it will cost. As both quantities
increase, the ratio stays the same.
ii No As the years go by the value of a house may go up or down. The ratio
does not stay the same.
b 1.5 ÷ 12 = 0.125 kg First, use division to find the mass of one sausage.
0.125 × 16 = 2 kg Now use multiplication to find the mass of 16 sausages.
c 500 g box: Compare the same quantity of cereal to work out which is the better value.
$3.20 ÷ 5 = $0.64/100 g Divide the cost by 5 to work out the price of 100 g of cereal.
200 g box:
$1.30 ÷ 2 = $0.65/100 g Divide the cost by 2 to work out the price of 100 g of cereal.
500 g box is better value. $0.64 < $0.65, so the bigger box is better value for money.
d i 200 × 0.76 = €152 Multiply the number of dollars by the exchange rate to convert to euros.
ii 19 ÷ 0.76 = $25 Divide the number of euros by the exchange rate to convert to dollars.

) Exercise 14.2

1 Are these quantities in direct proportion? Explain your answers.
a the total cost of cartons of orange juice and the number of cartons bought
b the number of girls in a school and the number of boys in a school
c the total cost of cinema tickets and the number of tickets bought
d the distance travelled in a car and the number of litres of fuel used by the car during the journey
e the number of goals scored by a football team and the number of supporters watching the match
f the amount of work a person does in a day and the number of cups of coffee they drink

138 14 Ratio and proportion