Question

Edna, Fatimah and Toby had a sum of money. The amount of money Edna had was 4 times the amount of money Fatimah had. The ratio of the amount of money Fatimah had to the total amount of money Toby and Fatimah had was 5:8. After Fatimah gave $30 to Toby, Toby had as much money as Fatimah. How much more money did Edna have than Toby in the end?

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Answer 1

Edna had $510 more amount of money than Toby in the end.

Explanation:

LET :-

Edna's amount of money - x

Fatimah's amount of money - y

Toby's amount of money - z

Now,

By the question,

x = 4y

y : (y + z) = 5 : 8

y - 30 = z + 30

Now,

y : (y + z) = 5 :8

or, y/(y + z) = 5/8

or, 8y = 5y + 5z

or, 3y = 5z

so, y = 5z/3

Now,

y - 30 = z + 30

or, 5z/3 - 30 = z + 30

or, (5z - 90)/3 = z + 30

or, 5z - 90 = 3z + 90

or, 5z - 3z = 90 + 90

or, 2z = 180

so, z = 90

Toby's amount of money - $90

Now,

y = 5z/3

or, y = 5 * 90/3

or, y = 5 * 30

so, y = 150

Fatimah's amount of money - $150

Again,

x = 4y

or, x = 4*150

or, x = 600

Edna's amount of money - $600

Now,

$600 - $90

= $510

Therefore,Edna had $510 more amount of money than Toby in the end.