Question

how many ounces (oz) of peanuts must be added to 14 oz of mixed nuts containing 20% peanuts to make a mixture with 44% peanuts?
4 oz
5 oz
6 oz
9 oz

Explanation:

Step1: Calculate initial peanuts amount

The initial 14 - oz mixed nuts have 20% peanuts. So the amount of peanuts initially is $14\times0.2 = 2.8$ oz. Let $x$ be the amount of peanuts (in oz) to be added.

Step2: Set up equation based on percentage

The total weight of the new mixture is $(14 + x)$ oz, and the amount of peanuts in the new mixture is $(2.8+x)$ oz. We want the new mixture to be 44% peanuts. So the equation is $\frac{2.8 + x}{14 + x}=0.44$.

Step3: Solve the equation

Multiply both sides by $(14 + x)$: $2.8+x=0.44(14 + x)$.
Expand the right - hand side: $2.8+x = 6.16+0.44x$.
Subtract $0.44x$ from both sides: $x-0.44x=6.16 - 2.8$.
Combine like terms: $0.56x=3.36$.
Divide both sides by 0.56: $x=\frac{3.36}{0.56}=6$ oz.

Answer:

C. 6 oz