A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 25% real fruit juice and Drink B contains 20% real fruit juice. Company made 280 liters of fruity drinks with 61 liters of real fruit juice. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 25% real fruit juice and Drink B contains 20% real fruit juice. Company made 280 liters of fruity drinks with 61 liters of real fruit juice. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
Let's call the number of liters of Drink A produced as 'x' and the number of liters of Drink B produced as 'y'.
Since Drink A contains 25% real fruit juice, 'x' liters of Drink A would contribute (25/100)*x = 0.25x liters of real fruit juice.
Similarly, since Drink B contains 20% real fruit juice, 'y' liters of Drink B would contribute (20/100)*y = 0.20y liters of real fruit juice.
According to the given information, the total amount of real fruit juice produced is 61 liters. Therefore, we can set up the following system of equations to represent the situation:
Equation 1: 0.25x + 0.20y = 61 (equation representing the total amount of real fruit juice produced)
Equation 2: x + y = 280 (equation representing the total amount of fruity drinks produced)
In this system, 'x' represents the number of liters of Drink A made, 'y' represents the number of liters of Drink B made, and the equations explain the relationships between the quantities involved.
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A = liters of drink A , B = liters of drink B
A + B = 280
.25 A + .20 B = 61 ... multiplying by 4 ... A + .8 B = 244
subtracting equations (to eliminate A) ... .2 B = 36
solve for B , then substitute back to find A