Solving a Party Mix Mixture Problem
Apply the seven-step problem-solving strategy to a mixture word problem involving a known total amount and two ingredients with given per-unit costs.
Problem: Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a pound. Orlando wants to make pounds of party mix at a cost of $6.50 a pound. How many pounds of nuts and how many pounds of cereal squares should he use?
- Read the problem and identify the ingredient types: nuts (value $7 per pound) and cereal squares (value $4 per pound). The total mixture weight is pounds at $6.50 per pound.
- Identify what to find: the number of pounds of nuts and the number of pounds of cereal squares.
- Name the unknowns using a single variable and the known-total technique. Let = the number of pounds of nuts. Then the number of pounds of cereal squares is . Organize in a table:
| Type | Pounds | Price per pound ($) | Total Value ($) |
|---|---|---|---|
| Nuts | |||
| Cereal squares | |||
| Party mix |
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Translate into an equation. The value of the nuts plus the value of the cereal squares equals the value of the party mix:
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Solve the equation:
- Distribute :
- Combine like terms:
- Subtract from both sides:
- Divide both sides by : Find the number of pounds of cereal squares: .
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Check: ✓
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Answer: Orlando should use pounds of nuts and pounds of cereal squares.
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