Page 148 - MAT KS3 Y8 Cambridge CheckPoint

14.3 Solving problems

5 A fruit dessert contains raspberries and strawberries in the ratio 1 : 2.
There are 400 g of strawberries in the dessert.
a How many grams of raspberries are there in the dessert?
b How much fruit is there altogether in the dessert?

6 Xavier and Alicia share some money in the ratio 3 : 5.
Xavier gets $75.
a How much does Alicia get?
b How much money do they share?
7 Kaya and Akiko share their electricity bills in the ratio 4 : 3.
In January Akiko pays $18.
a How much does Kaya pay?
b What is their total bill?
8 Three children share some sweets in the ratio of their ages.
The children are 4, 7 and 9 years old.
The oldest child gets 54 sweets.
a How many sweets do the other children get?
b How many sweets do they share?

9 When Alicia makes oat biscuits she uses syrup, butter and oats in the ratio 1 : 2 : 4.

I have plenty of syrup, but only 250 g of butter
and 440 g of oats in my kitchen cupboard.

Alicia makes as many oat biscuits as she can with these ingredients.
How much of each ingredient does she use?
10 Xavier makes some green paint.
He mixes yellow, blue and white paint in the ratio 4 : 5 : 1.
He uses 750 ml of blue paint.
How much green paint does he make?

Summary

You should now know that: You should be able to:
★ You can simplify a ratio by dividing the numbers in ★ Simplify ratios, including those expressed in
the ratio by the highest common factor. different units.
★ When you simplify a ratio you must make sure that ★ Divide a quantity into more than two parts in a
all the quantities are in the same units. given ratio.
★ When you share an amount in a given ratio you ★ Use the unitary method to solve simple problems
must divide the amount by the total number of involving ratio and direct proportion.
parts to find the value of one part. Then multiply ★ Mentally solve simple word problems, including
the value of one part by each number in the ratio. direct proportion problems.
★ Two values are in direct proportion when they
increase or decrease in the same ratio.

146 14 Ratio and proportion