The ratio of the volume of fruit juice to the volume of smoothie at a party was 4.5 : 2.4. there were 35 liters more fruit juice served than smoothies. find the volume of smoothies served

X=volume in liters of frut juice.
y=volume in liters of smoothies.
We can suggest the following system of equations:

x=y+35
x/y=4.5/2.4

We can solve this system by substituion method.
(y+35)/y=4.5/2.4
2.4(y+35)=4.5y
2.4y+84=4.5y
4.5y-2.4y=84
2.1y=84
y=84/2.1
y=40

x=y+35
x=40+35
x=75

The volume of smoothies served was 40 liters.