Question

Colin, Sara and Gordon share some sweets in the ratio 5:2:1. Colin gets 36 more sweets than Gordon. How many sweets are there altogether?

Answer 1

c=36+g

c:g:s=5:2:1

The ratio gives us two equations so that's three equations in three unknowns.  Actually we're after the total t; let's put that in to solve for directly.

c:g:s:t = 5 : 2 : 1 : 5+2+1

We turn the ratio to fraction equations.  s has the one; let's write everything in terms of s.

c/s = 5/1,  g/s = 2/1, t/s = 8/1

Clearing the fractions,

c = 5s, g = 2s, t = 8s

Our other equation is

c = 36 + g

Substituting in for c and g,

5s = 36 + 2s

Solving,

3s = 36

s = 12

That's right; let's just get the total t.

t = 8s = 72

Answer: 72