Worksheet on dividing amounts into ratios, featuring problems with real-life scenarios like sharing money and mixing materials.

Here are the step-by-step solutions for each problem on the worksheet.

a. £60 is to be shared between Gary and Susan in the ratio 2 : 3. How much does Susan receive?

1. Find the total number of parts: Add the numbers in the ratio together.
$2 + 3 = 5$ parts total.
2. Find the value of one part: Divide the total amount of money by the total number of parts.
$£60 \div 5 = £12$ per part.
3. Calculate Susan's share: Susan gets 3 parts (from the ratio 2:3).
$3 \times £12 = £36$.

b. Split £80 into two groups where one group is 3 times as big as the other.

1. Determine the ratio: If one group is 3 times bigger than the other, the ratio is 1 : 3.
2. Find the total number of parts:
$1 + 3 = 4$ parts total.
3. Find the value of one part: Divide the total money by the total parts.
$£80 \div 4 = £20$ per part.
4. Calculate the two groups:
* Small group (1 part): $1 \times £20 = £20$
* Big group (3 parts): $3 \times £20 = £60$

c. Carol and Tim received some money in the ratio 5 : 4. Tim received £60, how much was Carol's share?

1. Identify who has which part: The ratio is Carol : Tim (5 : 4). This means Tim represents the "4" part.
2. Find the value of one part: We know Tim's 4 parts equal £60.
$£60 \div 4 = £15$ per part.
3. Calculate Carol's share: Carol represents the "5" part.
$5 \times £15 = £75$.

d. To make concrete Alan mixes sand, cement and gravel in the ratio 3 : 1 : 4. He has 10kg of gravel. How much sand and cement should he use?

*Note: The order given is Sand : Cement : Gravel.*

1. Identify the known value: We know the amount of Gravel is 10kg. In the ratio (3 : 1 : 4), Gravel is the last number, which is 4.
2. Find the value of one part:
$10\text{kg} \div 4 = 2.5\text{kg}$ per part.
3. Calculate Sand: Sand is the first number (3).
$3 \times 2.5\text{kg} = 7.5\text{kg}$.
4. Calculate Cement: Cement is the middle number (1).
$1 \times 2.5\text{kg} = 2.5\text{kg}$.

e. Helen and Ann shared a box of sweets in the ratio 4 : 7. Ann got 12 more sweets than Helen. How many sweets did Ann have?

1. Find the difference in parts: Look at the ratio Helen : Ann (4 : 7).
$7 - 4 = 3$ parts difference.
2. Find the value of one part: We know the actual difference is 12 sweets. So, those 3 parts equal 12 sweets.
$12 \div 3 = 4$ sweets per part.
3. Calculate Ann's share: Ann has 7 parts.
$7 \times 4 = 28$ sweets.

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Final Answer:
a. £36
b. £20 and £60
c. £75
d. Sand: 7.5kg, Cement: 2.5kg
e. 28 sweets