how much of a(n) 80% orange juice drink must be mixed with 5 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice?

the amount of 80% orange juice drink is gallons.
(type an integer or a decimal.)

Question

how much of a(n) 80% orange juice drink must be mixed with 5 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice?

the amount of 80% orange juice drink is   gallons.
(type an integer or a decimal.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Mixture Problems" ], "current_concepts": [ "Linear Equations", "Mixture Problems" ] } ## Define the variable and set up the mixture equation $$ \begin{aligned} &\text{Let } x \text{ be the gallons of } 80\% \text{ orange juice drink.}\ &0.80x + 0.20(5) = 0.50(x + 5) \end{aligned} $$ ## Solve the linear equation for x $$ \begin{aligned} &0.80x + 1 = 0.50x + 2.5\ &0.30x = 1.5\ &x = 5 \end{aligned} $$ How much of a(n) 80% orange juice drink must be mixed with 5 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice? The amount of 80% orange juice drink is 5 gallons. (Type an integer or a decimal.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Define the variable and set up the mixture equation

Solve the linear equation for x

Answer: