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

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

Answer 2

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 $\frac{3x}{20}$ ,

Ben's share = $\frac{7x}{20}$

Cheryl's share = $\frac{10x}{20}$

As, Ben receives £650 more than Ann

$\frac{7x}{20}=\frac{3x}{20}+650$

$7x=3x+13000$

$4x=13000$

$x=3250$

So, Ann's share = $\frac{3*3250}{20}$ = £487.50

Ben's share = $\frac{7*3250}{20}$ =£1137.50

Cheryl's share = $\frac{10*3250}{20}$ = £1625

$487.50+1137.50+1625=3250$

Hence, the total amount of money shared is £3250