Digital SATMath: AlgebraMedium
A chef is mixing a special sauce. She needs to combine two ingredients, A and B. Ingredient A costs $3 per ounce, and Ingredient B costs $5 per ounce. If she wants to make 20 ounces of sauce that costs exactly $4.20 per ounce, how many ounces of Ingredient A should she use?
- A10 ounces
- B12 ounces
- C8 ounces
- D15 ounces
Show answer & explanationAnswer & explanation
Correct answer: C. 8 ounces
Let 'x' be the ounces of Ingredient A and 'y' be the ounces of Ingredient B. We have two equations: x + y = 20 (total ounces) and 3x + 5y = 20 * 4.20 (total cost). This simplifies to 3x + 5y = 84. From the first equation, y = 20 - x. Substitute this into the second: 3x + 5(20 - x) = 84. This gives 3x + 100 - 5x = 84, so -2x = -16, and x = 8.
Why the other options are wrong
- A. This would mean equal parts, which wouldn't result in the target cost per ounce.
- B. This would mean more of the cheaper ingredient, leading to a lower average cost.
- D. This would mean significantly more of the cheaper ingredient, leading to an even lower average cost.
Mixture Problems (Systems)
Problems involving combining two or more quantities with different properties (e.g., cost, concentration) to achieve a desired overall property.
- Typically involve two equations: one for total quantity and one for total value/concentration.
- Can be solved using substitution or elimination methods.
- Define variables clearly for each unknown quantity.
Memory trick: Quantity + Value equations, then Substitute to Solve.