math question in ratio

Question

A juice vendor has 3 cans of juice. The first contains 35% ice and the rest juice. The second contains 40% ice. How much juice should he mix from each of the containers so as to get 22 litres of juice such that the ratio of ice to juice is 3 : 5.

Answer 1

11. liters of 35% ice mixed with

11 liters of 40% ice to get 22 liters of 37.5% ice ratio of 3:5 is 3/3+5) = 3/8 = .375 =37.5% ice

3:5 is 3/8 ice = 37.5% ice

40-37.5 = 2.5

37.5 -35 = 2.5

they're equally distant from 37.5% so equal amounts of each are needed = 22/2 = 11 liters each

.35(11) + .4(11)

= 3.85 + 4.4

= 8.25 liters ice

.375(22) = 8.25 liters ice

more customary way to solve the problem is set up an equation

.35x + .40(22-x) = .375(22),

expand, combine like terms and solve for x = liters of 35% ice

22-x = liters of 40% ice