The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 60% pure fruit juice. The company is attempting to produce a fruit drink that contains 55% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 55% pure fruit juice?

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 60% pure fruit juice. The company is attempting to produce a fruit drink that contains 55% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 55% pure fruit juice?

Answer 1

Let x be the number of pints of the first type of fruit drink.

The number of pints of the second type of fruit drink is 140 - x.
40% of x pints of the first type of fruit drink is 0.4*x pints of pure fruit juice.
60% of (140 - x) pints of the second type of fruit drink is 0.6 * (140 - x) = 84 - 0.6x pints of pure fruit juice, since the second type of fruit drink is 60% pure fruit juice.
The resulting mixture contains (0.4x + 84 - 0.6x) = 84 - 0.2x pints of pure fruit juice.
The resulting mixture must contain 55% pure fruit juice, which can be written as 0.55 * 140 = 77 pints of pure fruit juice.
Therefore, 84 - 0.2x = 77.
Subtracting 84 from both sides of the equation, we get -0.2x = -7.
Dividing both sides of the equation by -0.2, we get x = -7 / -0.2 which simplifies to x = 35.
Therefore, 35 pints of the first type of fruit drink must be used, and since the total amount is 140 pints, the remaining 140 - 35 = <<140-35=105>>105 pints must be of the second type of fruit drink should be used. Answer: \boxed{35}.

Answer 2

To solve this problem, let's denote:

x = the number of pints of the first type of fruit drink (40% pure fruit juice)
y = the number of pints of the second type of fruit drink (60% pure fruit juice)

We know that the company wants to create a mixture that contains 140 pints and is 55% pure fruit juice.

From the problem, we can set up two equations based on the amount of pure fruit juice in each type of drink:

Equation 1: 0.4x (40% pure fruit juice in the first type of drink)
Equation 2: 0.6y (60% pure fruit juice in the second type of drink)

We can also set up an equation based on the total pints in the mixture:

Equation 3: x + y = 140 (total pints in the mixture)

Now, we can set up an equation based on the desired concentration of 55% pure fruit juice in the final mixture:

Equation 4: (0.4x + 0.6y) / 140 = 0.55 (concentration of pure fruit juice in the final mixture)

Now, let's solve these equations step by step:

Equation 1: 0.4x
Equation 2: 0.6y
Equation 3: x + y = 140
Equation 4: (0.4x + 0.6y) / 140 = 0.55

To solve for x and y, we can rearrange Equation 4 to:

0.4x + 0.6y = 140 * 0.55
0.4x + 0.6y = 77

Next, we can multiply Equation 3 by 0.4 to get:

0.4x + 0.4y = 0.4 * 140
0.4x + 0.4y = 56

Now, subtract this equation from the rearranged Equation 4:

(0.4x + 0.6y) - (0.4x + 0.4y) = 77 - 56
0.2y = 21

Divide both sides by 0.2:

y = 21 / 0.2
y = 105

Now, substitute this value of y back into Equation 3 to solve for x:

x + 105 = 140
x = 140 - 105
x = 35

Therefore, you would need 35 pints of the first type of fruit drink (40% pure fruit juice) and 105 pints of the second type of fruit drink (60% pure fruit juice) to make 140 pints of a mixture that is 55% pure fruit juice.