Question

A sum of money is divided amongst Farah, Shaiyara and Zahin in the ratio 10: 7: 5. If

Shaiyara gets $20 more than Zahin, find the total sum of money shared and the amount
Farah gets.

Answer 1

Answers:

• Total amount of money = 220 dollars
• Amount Farah gets = 100 dollars

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Step-by-step explanation:

• F = amount Farah gets
• S = amount Shaiyara gets
• Z = amount Zahin gets

The money is divided in the ratio 10:7:5

This means that

• F = 10x
• S = 7x
• Z = 5x

for some positive real number x.

Since Shaiyara gets $20 more than Zahin, we can say,

S = Z+20

Let's plug in S = 7x and Z = 5x and solve for x

S = Z+20

7x = 5x+20

7x-5x = 20

2x = 20

x = 20/2

x = 10

Therefore,

• F = 10x = 10*10 = 100
• S = 7x = 7*10 = 70
• Z = 5x = 5*10 = 50

The ratio F:S:Z becomes 100:70:50 which reduces fully to 10:7:5 after dividing all three parts by the GCF 10.

The total sum of money shared is 100+70+50 = 220 dollars and Farah gets $100 of that total.