Question

marshall bought 32 ounces of mixed nuts, which are estimated to be 30% peanuts. which expression can be used to find the percentage of peanut concentration of the final mix if he adds x ounces of peanuts?
y = \frac{0.3(32)+x}{32+x} \cdot 100
y = \frac{0.3(32)+0.3x}{32} \cdot 100
y = \frac{0.3(32)+x}{32} \cdot 100
y = \frac{0.3(32)+0.3x}{32+x} \cdot 100

Explanation:

Step1: Find initial peanuts

Initial mixed nuts: 32 oz, 30% peanuts. So initial peanuts: $0.3\times32$ oz.

Step2: Find final peanuts

Add \( x \) oz peanuts, so final peanuts: \( 0.3(32) + x \) oz.

Step3: Find final total

Final total mix: \( 32 + x \) oz (initial + added).

Step4: Percentage formula

Percentage = (Peanuts / Total) × 100. So \( y = \frac{0.3(32) + x}{32 + x} \times 100 \).

Answer:

\( y = \frac{0.3(32) + x}{32 + x} \cdot 100 \) (the first expression)