Question

A 19-liter mixture consists by volume of 1 part juice to 18 parts water. If x liters of juice and y liters of water are added to this mixture to make a 54-liter mixture consisting by volume of 1 part juice to 2 parts water, what is the value of x. I'm not sure, but would it be 27?

Answer 1

let x = volume of juice
let y = volume of water

Volume of Mixture
(x + 1) + (y + 18) = 54

solve for y

y = 35 - x

"1 part juice to 2 parts water"
ratio of juice to water = 1/2

(x + 1) / (y + 18) = 1/2

(x + 1) / ([35 - x] + 18) = 1/2

solve for x

x + 1 = 1/2 (53 - x)
2x + 2 = 53 - x
3x + 2 = 53
3x = 51
x = 17