Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 55% 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 60 pints of a mixture that is 40% pure fruit juice?

Answer 1

Let's use the method of setting up a system of equations to solve this problem.

Let x be the number of pints of the first type of fruit drink (30% pure), and y be the number of pints of the second type of fruit drink (55% pure). We want to find the values of x and y that will produce 60 pints of a mixture that is 40% pure.

We can start by setting up two equations based on the information given:

Equation 1: x + y = 60 (since we want to produce 60 pints of the mixture)

Equation 2: 0.3x + 0.55y = 0.4(60) (since we want the mixture to be 40% pure)

Simplifying Equation 2, we get:

0.3x + 0.55y = 24

Now we have a system of two equations with two unknowns:

x + y = 60

0.3x + 0.55y = 24

We can solve this system using substitution or elimination. Here, we'll use substitution:

Solving Equation 1 for x, we get x = 60 - y. Substituting this expression for x in Equation 2, we get:

0.3(60 - y) + 0.55y = 24

Expanding and simplifying, we get:

18 - 0.3y + 0.55y = 24

Combining like terms, we get:

0.25y = 6

Dividing by 0.25, we get:

y = 24

Substituting this value of y back into x + y = 60, we get:

x + 24 = 60

Solving for x, we get:

x = 36

Therefore, we need 36 pints of the 30% pure fruit drink and 24 pints of the 55% pure fruit drink to make 60 pints of a mixture that is 40% pure.