Question

The royal fruit company produces 2 types of drinks. The first type is 35% pure fruit juice,and the second type is 85%pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each of the two existing type of drink must be used to make 150pints of a mixture that is 75% pure fruit juice

Answer 1

A


Let x be the number of pints of the first type of drink (35% pure fruit juice), and y be the number of pints of the second type of drink (85% pure fruit juice).

We know that the total number of pints of the mixture is 150:

x + y = 150

We also know that the mixture is 75% pure fruit juice:

0.35x + 0.85y = 0.75(150)

Simplifying the second equation:

0.35x + 0.85y = 112.5

Multiplying the first equation by 0.35:

0.35x + 0.35y = 52.5

Subtracting this equation from the second equation:

0.5y = 60

y = 120

Substituting y = 120 into the first equation:

x + 120 = 150

x = 30

Therefore, the company needs to use 30 pints of the first type of drink and 120 pints of the second type of drink to make 150 pints of a mixture that is 75% pure fruit juice.

Answer 2

We should use 30 pints of the first drink and 120 pints of the second drink

Explanation:

Let x represent the number of pints of the first drink used
Volume of fruit juice in x pints = 35% of x = 0.35x

Let y represent the number of pints of the second drink used
Volume of fruit juice in y pints = 85% of y= 0.85y

Since the final mixture volume is 150 pints we get
x + y = 150 ..... [1]

If the final mixture has to contain 75% pure fruit juice, the volume of fruit juice in the mixture = 0.75 x 150 = 112.5 pints

Therefore
0.35x + 0.85y = 112.5 ...[2]

We will solve this set of simultaneous equations by making the coefficients of one of the variables equal and then subtracting to eliminate that variable

Multiply equation [1] by 0.35 to get the x coefficients equal

0.35 x [1]
=> 0.35(x + y) = 0.35(150)

=> 0.35x + 035y = 52.5 ... [3]

Subtract [3] from [2]:

[3] - [2] =>

0.35x + 0.85y - (0.35x + 035y) = 112.5 - 52.5

0.35x + 0.85y - 0.35x - 0.35y = 60

0x + 0.5y = 60

0.5y = 60

y = 60/0.5

y = 120

Therefore x = 150 - 120 = 30

Therefore we should use 30 pints of the first drink and 120 pints of the second drink