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