Question

Ann Ben and cheyrl share some money in the ratio 3:7:10 Ben receives £650 more than Ann calculate the total amount of money that they shared

Answer 1

Let the total money the friends shared be = x

As given, the ratio is : 3:7:10

So, Total =20

So Ann's share is
`(3x)/(20)` ,

Ben's share =
`(7x)/(20)`

Cheryl's share =
`(10x)/(20)`

As, Ben receives £650 more than Ann

`(7x)/(20)=(3x)/(20)+650`

`7x=3x+13000`

`4x=13000`

`x=3250`

So, Ann's share =
`(3*3250)/(20)` = £487.50

Ben's share =
`(7*3250)/(20)` =£1137.50

Cheryl's share =
`(10*3250)/(20)` = £1625

`487.50+1137.50+1625=3250`

Hence, the total amount of money shared is £3250

Answer 2

Let

x------------> Ann's amount of money

y------------> Ben's amount of money

z------------> Cheryl's amount of money

we know that

y=x+650-----> equation 1

x/y=3/7------> y=(7/3)*x-----> equation 2

y/z=7/10-----> equation 3

x/z=3/10-----> equation 4

equate equation 1 and equation 2

x+650=(7/3)*x------> multiply by 3-----> 3x+1950=7x----> 4x=1950

x=1950/4-----> x=487.5

y=x+650-----> y=487.5+650-----> y=1137.5

y/z=7/10------> z/y=10/7------> z=(10/7)*1137.5-----> z=1625

the answer is

Ann's amount of money is £487.5

Ben's amount of money is £1137.5

Cheryl's amount of money is £1625

487.5+1137.5+1625=£3250

The total of money shared is £3250