Ratio and Proportion - Free resources about circles and their ... - Free Printable

Let's solve each problem step by step.

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Problem 1: Split £150 into the following ratios

#### a. 2:1
- Total parts = 2 + 1 = 3
- Value of one part = \( \frac{150}{3} = 50 \)
- Split:
- First part (2 parts) = \( 2 \times 50 = 100 \)
- Second part (1 part) = \( 1 \times 50 = 50 \)
- Answer: £100 : £50

#### b. 1:4
- Total parts = 1 + 4 = 5
- Value of one part = \( \frac{150}{5} = 30 \)
- Split:
- First part (1 part) = \( 1 \times 30 = 30 \)
- Second part (4 parts) = \( 4 \times 30 = 120 \)
- Answer: £30 : £120

#### c. 3:7
- Total parts = 3 + 7 = 10
- Value of one part = \( \frac{150}{10} = 15 \)
- Split:
- First part (3 parts) = \( 3 \times 15 = 45 \)
- Second part (7 parts) = \( 7 \times 15 = 105 \)
- Answer: £45 : £105

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Problem 2: Split 360g into the following ratios

#### a. 3:1
- Total parts = 3 + 1 = 4
- Value of one part = \( \frac{360}{4} = 90 \)
- Split:
- First part (3 parts) = \( 3 \times 90 = 270 \)
- Second part (1 part) = \( 1 \times 90 = 90 \)
- Answer: 270g : 90g

#### b. 5:7
- Total parts = 5 + 7 = 12
- Value of one part = \( \frac{360}{12} = 30 \)
- Split:
- First part (5 parts) = \( 5 \times 30 = 150 \)
- Second part (7 parts) = \( 7 \times 30 = 210 \)
- Answer: 150g : 210g

#### c. 2:4:3
- Total parts = 2 + 4 + 3 = 9
- Value of one part = \( \frac{360}{9} = 40 \)
- Split:
- First part (2 parts) = \( 2 \times 40 = 80 \)
- Second part (4 parts) = \( 4 \times 40 = 160 \)
- Third part (3 parts) = \( 3 \times 40 = 120 \)
- Answer: 80g : 160g : 120g

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Problem 3: Split 225m into the following ratios

#### a. 11:4
- Total parts = 11 + 4 = 15
- Value of one part = \( \frac{225}{15} = 15 \)
- Split:
- First part (11 parts) = \( 11 \times 15 = 165 \)
- Second part (4 parts) = \( 4 \times 15 = 60 \)
- Answer: 165m : 60m

#### b. 5:1:3
- Total parts = 5 + 1 + 3 = 9
- Value of one part = \( \frac{225}{9} = 25 \)
- Split:
- First part (5 parts) = \( 5 \times 25 = 125 \)
- Second part (1 part) = \( 1 \times 25 = 25 \)
- Third part (3 parts) = \( 3 \times 25 = 75 \)
- Answer: 125m : 25m : 75m

#### d. 10:9:6
- Total parts = 10 + 9 + 6 = 25
- Value of one part = \( \frac{225}{25} = 9 \)
- Split:
- First part (10 parts) = \( 10 \times 9 = 90 \)
- Second part (9 parts) = \( 9 \times 9 = 81 \)
- Third part (6 parts) = \( 6 \times 9 = 54 \)
- Answer: 90m : 81m : 54m

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Problem 4: Karen and Priti are sharing a packet of sweets in the ratio 2:3. Karen gets 10 sweets. How many sweets does Priti get?

- Ratio of sweets = 2:3
- Let the number of sweets Karen gets be \( 2x \) and the number of sweets Priti gets be \( 3x \).
- Given: \( 2x = 10 \)
- Solve for \( x \):
\[
x = \frac{10}{2} = 5
\]
- Number of sweets Priti gets = \( 3x = 3 \times 5 = 15 \)
- Answer: 15 sweets

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Problem 5: Tom, Phil, and Ali deliver newspapers in the ratio 1:4:3. They delivered 120 newspapers in total. How many newspapers did Ali deliver?

- Ratio of newspapers delivered = 1:4:3
- Total parts = 1 + 4 + 3 = 8
- Value of one part = \( \frac{120}{8} = 15 \)
- Newspapers delivered by Ali (3 parts) = \( 3 \times 15 = 45 \)
- Answer: 45 newspapers

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Problem 6: Ando and Hiro are 13 and 15 respectively. Their grandad gives them £112 to share in the ratio of their ages. How much do they each get?

- Ages of Ando and Hiro = 13 and 15
- Ratio of their ages = 13:15
- Total parts = 13 + 15 = 28
- Value of one part = \( \frac{112}{28} = 4 \)
- Amount Ando gets (13 parts) = \( 13 \times 4 = 52 \)
- Amount Hiro gets (15 parts) = \( 15 \times 4 = 60 \)
- Answer: Ando gets £52, Hiro gets £60

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Problem 7: There are 12 people in a book club. The ratio of men to women is 1:2. Two more men join the group. What is the new ratio of men to women?

- Initial total people = 12
- Ratio of men to women = 1:2
- Let the number of men be \( x \) and the number of women be \( 2x \).
- Total people: \( x + 2x = 3x = 12 \)
- Solve for \( x \):
\[
x = \frac{12}{3} = 4
\]
- Initial number of men = \( x = 4 \)
- Initial number of women = \( 2x = 8 \)
- After two more men join:
- New number of men = \( 4 + 2 = 6 \)
- Number of women remains the same = 8
- New ratio of men to women = \( 6:8 \)
- Simplify the ratio:
\[
6:8 = \frac{6}{2} : \frac{8}{2} = 3:4
\]
- Answer: 3:4

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Problem 8: In a tennis club, there are 3 times as many right-handed players as left-handed players. If there are 36 players in total, how many are left-handed?

- Let the number of left-handed players be \( x \).
- Number of right-handed players = \( 3x \)
- Total players = \( x + 3x = 4x \)
- Given: \( 4x = 36 \)
- Solve for \( x \):
\[
x = \frac{36}{4} = 9
\]
- Number of left-handed players = \( x = 9 \)
- Answer: 9 players

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Final Answers:

1. a. £100 : £50
b. £30 : £120
c. £45 : £105

2. a. 270g : 90g
b. 150g : 210g
c. 80g : 160g : 120g

3. a. 165m : 60m
b. 125m : 25m : 75m
d. 90m : 81m : 54m

4. 15 sweets

5. 45 newspapers

6. Ando gets £52, Hiro gets £60

7. 3:4

8. 9 players

Boxed Final Answer:
\[
\boxed{9}
\]