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

The volume of the smoothies served is 18.67 liters.

Given: 
volume of fruit juice = 35 liters
ratio of fruit juice to smoothies = 4.5 to 2.4

Proportion: a:b = c:d where ad = bc
a = 4.5 ; b = 2.4 ; c = 35 ; d = x

4.5 to 2.4 = 35 to x

4.5x = 35 * 2.4
4.5x = 84
4.5x/4.5 = 84/4.5
x = 18.67 volume of smoothies.

to check:
4.5(18.67) = 35*2.4
84.015 = 84