Math

Question Three friends share £300 in the ratio 10:11:9. How much does each friend receive?

Studdy Solution

STEP 1

Assumptions
1. The total amount given is £300.
2. The ratio of the distribution is 10:11:9 for Simon, Sarah, and Matthew respectively.
3. The sum of the parts of the ratio will give us the total number of parts to divide the amount by.

STEP 2

First, we need to find the sum of the parts of the ratio. This will tell us how many parts the total amount of £300 will be divided into.
Sum of parts=Simon’s part+Sarah’s part+Matthew’s part\text{Sum of parts} = \text{Simon's part} + \text{Sarah's part} + \text{Matthew's part}

STEP 3

Now, plug in the values of the ratio into the sum.
Sum of parts=10+11+9\text{Sum of parts} = 10 + 11 + 9

STEP 4

Calculate the sum of the parts.
Sum of parts=10+11+9=30\text{Sum of parts} = 10 + 11 + 9 = 30

STEP 5

Now that we have the sum of the parts, we can find the value of one part by dividing the total amount by the sum of the parts.
Value of one part=Total amount/Sum of parts\text{Value of one part} = \text{Total amount} / \text{Sum of parts}

STEP 6

Plug in the values for the total amount and the sum of the parts to calculate the value of one part.
Value of one part=£300/30\text{Value of one part} = £300 / 30

STEP 7

Calculate the value of one part.
Value of one part=£300/30=£10\text{Value of one part} = £300 / 30 = £10

STEP 8

Now that we have the value of one part, we can find out how much each person receives by multiplying the value of one part by the number of parts each person gets according to the ratio.
For Simon: Simon’s amount=Simon’s part×Value of one part\text{Simon's amount} = \text{Simon's part} \times \text{Value of one part}

STEP 9

Calculate Simon's amount.
Simon’s amount=10×£10\text{Simon's amount} = 10 \times £10

STEP 10

Simon receives £100.
Simon’s amount=10×£10=£100\text{Simon's amount} = 10 \times £10 = £100

STEP 11

For Sarah: Sarah’s amount=Sarah’s part×Value of one part\text{Sarah's amount} = \text{Sarah's part} \times \text{Value of one part}

STEP 12

Calculate Sarah's amount.
Sarah’s amount=11×£10\text{Sarah's amount} = 11 \times £10

STEP 13

Sarah receives £110.
Sarah’s amount=11×£10=£110\text{Sarah's amount} = 11 \times £10 = £110

STEP 14

For Matthew: Matthew’s amount=Matthew’s part×Value of one part\text{Matthew's amount} = \text{Matthew's part} \times \text{Value of one part}

STEP 15

Calculate Matthew's amount.
Matthew’s amount=9×£10\text{Matthew's amount} = 9 \times £10

STEP 16

Matthew receives £90.
Matthew’s amount=9×£10=£90\text{Matthew's amount} = 9 \times £10 = £90
Simon receives £100, Sarah receives £110, and Matthew receives £90.

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