Question

a grocer combined walnuts that cost $2.90 per pound and cashews that cost $3.30 per pound with 28 lb of peanuts that cost $2.00 per pound. find the amount of walnuts and the amount of cashews used to make a 60 - pound mixture costing $2.64 per pound.
walnuts
lb
cashews
lb
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Explanation:

Step1: Find the weight of walnuts and cashews combined

The total mixture is 60 - pound and there are 28 pounds of peanuts. So the combined weight of walnuts and cashews is $60 - 28=32$ pounds. Let the weight of walnuts be $x$ pounds, then the weight of cashews is $(32 - x)$ pounds.

Step2: Set up an equation based on cost - value relationship

The cost of the mixture is based on the cost of each component. The total cost of the 60 - pound mixture at $2.64$ per pound is $60\times2.64 = 158.4$ dollars. The cost of peanuts is $28\times2=56$ dollars. The cost of walnuts is $2.9x$ dollars and the cost of cashews is $3.3(32 - x)$ dollars. So the equation is $56+2.9x + 3.3(32 - x)=158.4$.

Step3: Expand and simplify the equation

Expand $3.3(32 - x)$ to get $105.6-3.3x$. The equation becomes $56 + 2.9x+105.6-3.3x=158.4$. Combine like - terms: $(2.9x-3.3x)+(56 + 105.6)=158.4$, which simplifies to $-0.4x+161.6 = 158.4$.

Step4: Solve for $x$ (weight of walnuts)

Subtract 161.6 from both sides: $-0.4x=158.4 - 161.6=-3.2$. Then divide both sides by $-0.4$: $x=\frac{-3.2}{-0.4}=8$ pounds.

Step5: Find the weight of cashews

Since the combined weight of walnuts and cashews is 32 pounds and the weight of walnuts $x = 8$ pounds, the weight of cashews is $32 - 8 = 24$ pounds.

Answer:

walnuts: 8 lb
cashews: 24 lb