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
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 [tex]\frac{3x}{20}[/tex] ,
Ben's share = [tex]\frac{7x}{20}[/tex]
Cheryl's share = [tex]\frac{10x}{20}[/tex]
As, Ben receives £650 more than Ann
[tex]\frac{7x}{20}=\frac{3x}{20}+650[/tex]
[tex]7x=3x+13000[/tex]
[tex]4x=13000[/tex]
[tex]x=3250[/tex]
So, Ann's share = [tex]\frac{3*3250}{20}[/tex] = £487.50
Ben's share = [tex]\frac{7*3250}{20}[/tex] =£1137.50
Cheryl's share = [tex]\frac{10*3250}{20}[/tex] = £1625
[tex]487.50+1137.50+1625=3250[/tex]
Hence, the total amount of money shared is £3250
