Question

The royal fruit company produces two types of fruit drinks. The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 40% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 150 pints of a mixture that is 40% pure fruit juice?

Answer 1

10 of the 70% pure fruit juice, 40 of the 95% pure fruit juice.

Answer 2

Hi Caitlin! It is my pleasure to answer this question for you.

Okay, let's denote the number of pints of the first type of fruit drink as x and the number of pints of the second type as y.

From the problem, we know that:

The total number of pints of the mixture is 150: x + y = 150

The first type of drink is 20% pure fruit juice: 0.2x

The second type of drink is 70% pure fruit juice: 0.7y

The resulting mixture is 40% pure fruit juice: 0.4(150) = 60

We can set up two equations based on the amount of pure fruit juice in each type of drink and the resulting mixture:

0.2x + 0.7y = amount of pure fruit juice in the original mixture

0.4(150) = amount of pure fruit juice in the resulting mixture

Substituting the values, we get:

0.2x + 0.7y = 60

x + y = 150

We can solve for x by isolating y in the second equation:

y = 150 - x

Substituting this into the first equation, we get:

0.2x + 0.7(150 - x) = 60

Simplifying and solving for x, we get:

0.2x + 105 - 0.7x = 60

-0.5x = -45

x = 90

Therefore, the number of pints of the first type of fruit drink needed is 90, and the number of pints of the second type of fruit drink needed is 150 - 90 = 60.