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 create a system of equations based on the amounts of two drinks produced by a company, focusing on their percentages of real fruit juice. We need to determine the quantities of each drink and how they relate to the total fruit juice used.
Answer
The system of equations is: $$ \begin{align*} 0.2x + 0.1y &= 70 \\ x &= 3y \end{align*} $$
Answer for screen readers
The system of equations is given by:
$$ \begin{align*} 0.2x + 0.1y &= 70 \ x &= 3y \end{align*} $$
Steps to Solve
- Define the Variables
Let ( x ) represent the liters of Drink A produced and ( y ) represent the liters of Drink B produced.
- Set Up the First Equation
The problem states that the company used 70 liters of real fruit juice. Since Drink A contains 20% real fruit juice, the contribution from Drink A to the total juice used is ( 0.2x ). Drink B contains 10% real fruit juice, contributing ( 0.1y ). Thus, we can write the equation: $$ 0.2x + 0.1y = 70 $$
- Set Up the Second Equation
According to the statement, the company made 3 times as many liters of Drink A as liters of Drink B. This gives us the equation: $$ x = 3y $$
- System of Equations
Now we have a system of two equations based on the problem:
- ( 0.2x + 0.1y = 70 )
- ( x = 3y )
The system of equations is given by:
$$ \begin{align*} 0.2x + 0.1y &= 70 \ x &= 3y \end{align*} $$
More Information
This system allows for the determination of the quantities of Drinks A and B produced based on the constraints provided by the juice content and production ratios.
Tips
- Confusing the percentages in the equations; ensure to convert them correctly.
- Misunderstanding the relationship between the amounts of drinks; the phrasing "3 times as many" can be tricky, so clarify which drink is being compared.
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