Digital SATMath: Problem-Solving and Data AnalysisHard
A nutritionist is creating a meal plan. She wants to mix two types of grains: Grain X, which has 2 grams of protein per 100 grams, and Grain Y, which has 8 grams of protein per 100 grams. If she wants to create a 600-gram mixture that has a total of 30 grams of protein, how many grams of Grain Y should she use?
- A450 grams
- B300 grams
- C200 grams
- D150 grams
Show answer & explanationAnswer & explanation
Correct answer: B. 300 grams
Let x be the amount of Grain X and y be the amount of Grain Y. We have x + y = 600 (total grams). Protein from X = 0.02x, Protein from Y = 0.08y. Total protein: 0.02x + 0.08y = 30. From the first equation, x = 600 - y. Substitute into the second: 0.02(600 - y) + 0.08y = 30. 12 - 0.02y + 0.08y = 30. 0.06y = 18. y = 18 / 0.06 = 300 grams.
Why the other options are wrong
- A. This might come from an error in setting up the equations or solving the system, such as swapping the protein percentages or a calculation mistake.
- C. This might come from an incorrect setup or solving the system, possibly if one of the protein percentages was misapplied.
- D. This might come from an error in setting up the equations or solving the system, such as using incorrect percentages or miscalculations.
Mixture Problems (Systems of Equations)
Mixture problems involve combining two or more quantities with different properties to create a mixture with desired overall properties, typically solved using a system of linear equations.
- One equation usually represents the total quantity of the mixture.
- Another equation represents the total amount of a specific component (e.g., protein, concentration).
- Careful conversion of percentages or rates to decimals is crucial.
Memory trick: Total amount, total quality, two equations to find the mix.