Answer:
Now, substitute the value of y back into the first equation to find x:
x + 16 = 40
x = 40 - 16
x = 24
Therefore, the Royal Fruit Company should use 24 pints of the first type of fruit drink (60% pure fruit juice) and 16 pints of the second type of fruit drink (85% pure fruit juice) to make 40 pints of a mixture that is 70% pure fruit juice.
Explanation:
To determine how many pints of each type of fruit drink the Royal Fruit Company should use to create a 70% pure fruit juice mixture, we can set up a system of equations.
Let's say x represents the number of pints of the first type of fruit drink (60% pure fruit juice), and y represents the number of pints of the second type of fruit drink (85% pure fruit juice).
We know that the total amount of fruit drink needed is 40 pints, so we have the equation: x + y = 40.
We also know that the resulting mixture should be 70% pure fruit juice. To calculate the pure fruit juice content, we need to multiply the percentage by the number of pints. Thus, we have the equation: (0.60x + 0.85y)/40 = 0.70.
To solve this system of equations, we can use substitution or elimination. Let's use the substitution method:
From the first equation, we can rewrite it as x = 40 - y.
Substituting x in the second equation, we get: (0.60(40 - y) + 0.85y)/40 = 0.70.
Now, we can solve for y:
(24 - 0.60y + 0.85y)/40 = 0.70
(0.25y + 24)/40 = 0.70
0.25y + 24 = 0.70 * 40
0.25y + 24 = 28
0.25y = 28 - 24
0.25y = 4
y = 4 / 0.25
y = 16
Now, substitute the value of y back into the first equation to find x:
x + 16 = 40
x = 40 - 16
x = 24
Therefore, the Royal Fruit Company should use 24 pints of the first type of fruit drink (60% pure fruit juice) and 16 pints of the second type of fruit drink (85% pure fruit juice) to make 40 pints of a mixture that is 70% pure fruit juice.