3 : 7 = 9 : \hspace{0.8cm}
Worked Solution & Answer
7 × 3 = 21 B1
Answer: 21
Ratio — Notes & Worked Examples Show / Hide
Explanation:
Ratio questions come in three main types: given the total, given one part, or given the difference between two parts. Always ask yourself what the number in the question represents in parts, then divide to find the value of 1 part.
Once you know what 1 part is worth, multiply by the number of parts required to find each share. Always check your final answer by adding or subtracting the shares to make sure they match the information in the question.
Example 1: Share £140 between Amy and Ben in the ratio 2 : 5.
Total parts = 2 + 5 = 7; 1 part = £140 ÷ 7 = £20
Amy = 2 × £20 = £40; Ben = 5 × £20 = £100
Answer: £40 and £100
Example 2: Red and blue counters are in the ratio 3 : 7. There are 24 more blue than red counters. Find the total number of counters.
Solution:
Difference in parts = 7 − 3 = 4 parts
1 part = 24 ÷ 4 = 6 counters
Total parts = 3 + 7 = 10 parts
Total counters = 10 × 6 = 60
Answer: 60 counters
Sarah and Tom share some money in the ratio 4:7
Sarah receives £44
How much money does Tom receive?
Sarah receives £44
How much money does Tom receive?
£
Worked Solution & Answer
1) Add the ratio parts together
2) Divide the total by total parts to find 1 part, then multiply
£77
2) Divide the total by total parts to find 1 part, then multiply
£77
Answer: £ £77
Boris has made this pattern out of black and white squares:
4 black squares and 1 white square.
4 black squares and 1 white square.
Boris has to add more squares to make a new pattern.
He has to use the smallest possible number of extra squares.
25 of the new pattern is black.
How many black squares and white squares will there be in the new pattern?
He has to use the smallest possible number of extra squares.
25 of the new pattern is black.
How many black squares and white squares will there be in the new pattern?
Worked Solution & Answer
To minimize extra squares, keep the 4 black squares already present M1
If 4 black squares represent 25 of the new pattern:
Total squares = 4 ÷ 25 = 4 × 52 = 10 squares
White squares = 10 - 4 = 6 white squares
(Extra white squares added = 6 - 1 = 5). A1
If 4 black squares represent 25 of the new pattern:
Total squares = 4 ÷ 25 = 4 × 52 = 10 squares
White squares = 10 - 4 = 6 white squares
(Extra white squares added = 6 - 1 = 5). A1
Answer: Black squares: 4, White squares: 6
The ratio of the cost of one metre of cotton fabric to the cost of one metre of silk fabric is 2 : 5
Complete the table of costs.
Worked Solution & Answer
1 m cotton = £6 ÷ 2 = £3 M1
⇒ 6 m = £18, 8 m = £24, 9 m = £27. 1 m silk = (£3 ÷ 2) × 5 = £7.50 M1
⇒ 2 m = £15, 6 m = £45, 8 m = £60, 9 m = £67.50 A1
⇒ 6 m = £18, 8 m = £24, 9 m = £27. 1 m silk = (£3 ÷ 2) × 5 = £7.50 M1
⇒ 2 m = £15, 6 m = £45, 8 m = £60, 9 m = £67.50 A1
Answer: Cotton: (£6), £18, £24, £27; Silk: £15, £45, £60, £67.50
Information about two fridge-freezers, A and B, is shown.
- Fridge-freezer A: Total capacity is 330 litres; fridge capacity : freezer capacity = 3 : 2
- Fridge-freezer B: Fridge capacity is 294 litres; fridge capacity : freezer capacity = 7 : 3
Grace buys one of these fridge-freezers.
She buys the one with the greater freezer capacity.
- Fridge-freezer A: Total capacity is 330 litres; fridge capacity : freezer capacity = 3 : 2
- Fridge-freezer B: Fridge capacity is 294 litres; fridge capacity : freezer capacity = 7 : 3
Grace buys one of these fridge-freezers.
She buys the one with the greater freezer capacity.
Which one does she buy?
You must show your working.
You must show your working.
Answer
Worked Solution & Answer
Step 1: Freezer capacity for A: M1
Total parts = 3 + 2 = 5
Freezer capacity = 25 × 330 = 2 × 66 = 132 litres M1
Step 2: Freezer capacity for B:
7 parts = 294 litres ⇒ 1 part = 294 ÷ 7 = 42 litres
Freezer capacity = 3 × 42 = 126 litres M1
Step 3: Comparison:
132 > 126, so fridge-freezer A has the greater freezer capacity
Grace buys A. A1
Total parts = 3 + 2 = 5
Freezer capacity = 25 × 330 = 2 × 66 = 132 litres M1
Step 2: Freezer capacity for B:
7 parts = 294 litres ⇒ 1 part = 294 ÷ 7 = 42 litres
Freezer capacity = 3 × 42 = 126 litres M1
Step 3: Comparison:
132 > 126, so fridge-freezer A has the greater freezer capacity
Grace buys A. A1
Answer: Answer A
Shahid is going to use these instructions to make a fizzy drink.
(a) If Shahid is correct, what is the greatest amount of fizzy drink he can make? [3 marks]
ml
(b) Does this affect the greatest amount of fizzy drink he can make?
Give a reason for your answer. [1 mark]
Give a reason for your answer. [1 mark]
Worked Solution & Answer
(a)
300 ÷ 5 = 60 ml per part → needs 2 × 60 = 120 ml lemonade M2
total = 300 + 120 = 420 ml A1
total = 300 + 120 = 420 ml A1
Answer (a): 420 ml
(b)
No, 160 ml > 120 ml C1
Answer (b): No, because 300 ml of orange juice only requires 120 ml of lemonade, and he has 160 ml
Numbered discs are in two boxes.
(a) Work out the ratio
total value of the numbers in **Box A** : total value of the numbers in **Box B**
Give your answer in its simplest form. [3 marks]
total value of the numbers in **Box A** : total value of the numbers in **Box B**
Give your answer in its simplest form. [3 marks]
Answer
(b) One disc is picked at random from Box A.
Write down the probability that the number on the disc is greater than 6 [1 mark]
Write down the probability that the number on the disc is greater than 6 [1 mark]
Answer
Worked Solution & Answer
(a)
Total Box A = 2 + 2 + 3 + 4 + 9 = 20 M1
Total Box B = 1 + 1 + 1 + 2 + 3 + 4 + 4 + 9 = 25 M1
Ratio = 20 : 25 = 4 : 5 A1
Total Box B = 1 + 1 + 1 + 2 + 3 + 4 + 4 + 9 = 25 M1
Ratio = 20 : 25 = 4 : 5 A1
Answer (a): Answer 4 : 5
(b)
Box A has 5 discs
Only the disc with '9' is > 6, so probability = 1/5 B1
Only the disc with '9' is > 6, so probability = 1/5 B1
Answer (b): Answer 15
A bag contains only pink sweets, white sweets, green sweets and red sweets.
The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.
The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.
The ratio
number of pink sweets : number of white sweets = 2 : 1
There are 28 red sweets in the bag.
Work out the number of white sweets in the bag.
number of pink sweets : number of white sweets = 2 : 1
There are 28 red sweets in the bag.
Work out the number of white sweets in the bag.
Worked Solution & Answer
Total sweets = 28 ÷ 0.35 = 80 M2
P(pink or white) = 1 – (0.2 + 0.35) = 0.45 M1
Since pink : white = 2 : 1, P(white) = 0.45 ÷ 3 = 0.15 M1
Number of white sweets = 0.15 × 80 = 12 A1
P(pink or white) = 1 – (0.2 + 0.35) = 0.45 M1
Since pink : white = 2 : 1, P(white) = 0.45 ÷ 3 = 0.15 M1
Number of white sweets = 0.15 × 80 = 12 A1
Answer: 12
Scott wants to make orange juice.
He is going to buy boxes of oranges.
He is going to buy boxes of oranges.
(a) Work out the number of boxes of oranges that Scott needs to buy.
You must show all your working. [3 marks]
You must show all your working. [3 marks]
(b) Write down the ratio of the number of apples that Scott buys to the number of bananas that he buys.
Give your ratio in its simplest form. [2 marks]
Give your ratio in its simplest form. [2 marks]
Worked Solution & Answer
(a)
8 ÷ 2 = 4 M1
4 × 30 = 120 oranges needed M1
120 ÷ 24 = 5 boxes A1
4 × 30 = 120 oranges needed M1
120 ÷ 24 = 5 boxes A1
Answer (a): 5
(b)
1260 : 280 = 126 : 28 = 9 : 2 (dividing by 140) M1 A1
Answer (b): 9 : 2
Here is a list of ingredients needed to make 6 biscuits.
(a) How many biscuits does Asha make? [2 marks]
(b) What weight of butter does Julie use? [2 marks]
g
(c) How much does Julie pay? [2 marks]
rupees
Worked Solution & Answer
(a)
(450 ÷ 90) × 6 = 30 M1 A1
Answer (a): 30
(b)
(84 ÷ 6) × 75 = 14 × 75 = 1050 g M1 A1
Answer (b): 1050 g
(c)
(624 ÷ 8) × 5 = 78 × 5 = 390 rupees M1 A1
Answer (c): 390 rupees