ratio maths problem

Question

Liam, Sarah and Emily shared some money in the ratio 2 : 3 : 7
Emily got £80 more than Liam.
How much money did Sarah get?

Answer 1

Emily got 7x

Liam got 2x

7x = 2x + 80

5x = 80

x = 16

Liam got 32, Sarah got 48, and Emily got 112

Answer 2

I would start by breaking those ratios up into equations that we can use to plug in and solve to other equations.  If we know Emily has 7/2 more than Liam, then we can say...

 

e = 7/2*l

 

We are also given...

 

e = l + 80

 

So now we can solve for Liam.

 

e = l+ 80 = 7/2*l

80 = 7/2l - l

80 = 5/2*l

32 = l

 

So now we can get Emily's share:

 

e = l+80

e = 32+80

e=112

 

And since we know that Sarah gets 3/2 more than Liam, we can also get her share:

 

s = 3/2 * l

s = 3/2 * 32

s = 48

 

Finally, we can check these answers by making sure Emily and Sarah are at a 7:3 ratio.

 

e:s

112:48

(16*7):(16*3)

7:3