A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. The company used 70... A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. The company used 70 liters of real fruit juice to make 3 times as many liters of Drink A as liters of Drink B. 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.
Understand the Problem
The question is asking to formulate a system of equations based on the information given about two drinks, including their composition and the relationship between the quantities made. This involves defining variables for the quantities of the drinks and setting up equations to express the given relationships.
Answer
The equations are: \( 0.2x + 0.1y = 70 \) and \( x = 3y \).
Answer for screen readers
The system of equations that could be used is:
- ( 0.2x + 0.1y = 70 )
- ( x = 3y )
Steps to Solve
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Define the Variables
Let's define the variables for our equations.
Let ( x ) be the number of liters of Drink A made.
Let ( y ) be the number of liters of Drink B made. -
Set Up the Total Quantity Equation
According to the problem, the company used 70 liters of real fruit juice to make Drinks A and B.
The equation representing this relationship is:
$$ 0.2x + 0.1y = 70 $$
This shows that 20% of Drink A's volume contributes real fruit juice to the total, and 10% of Drink B does as well. -
Set Up the Relationship Between Drinks A and B
The problem states that the company made 3 times as many liters of Drink A as Drink B.
We can express this relationship with the equation:
$$ x = 3y $$ -
Formulate the System of Equations
Now we have a system of two equations:
- ( 0.2x + 0.1y = 70 )
- ( x = 3y )
These equations can be solved simultaneously to find the values of ( x ) and ( y ).
The system of equations that could be used is:
- ( 0.2x + 0.1y = 70 )
- ( x = 3y )
More Information
This system allows us to find the quantities of Drinks A and B based on the total amount of real fruit juice used and their ratio. By solving these equations, one can determine how many liters of each drink were made.
Tips
- Misunderstanding Percentages: Sometimes, people forget to convert percentages into decimal form when creating equations.
- Incorrect Relationships: Failing to correctly establish the relationship between the quantities of A and B can lead to incorrect equations.
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