Question

1. -/1 points peanuts sell for $5 per pound. cashews sell for $8 per pound. how many pounds of cashews should be mixed with 14 pounds of peanuts to obtain a mixture that has a value of $5.90 per pound? lb

Explanation:

Step1: Define variables for cashews

Let $x$ = pounds of cashews needed.

Step2: Set up total cost equation

Total cost of peanuts + total cost of cashews = total cost of mixture
$5 \times 14 + 8x = 5.90(14 + x)$

Step3: Simplify left side

Calculate cost of peanuts:
$70 + 8x = 5.90(14 + x)$

Step4: Expand right side

Distribute the 5.90:
$70 + 8x = 82.6 + 5.90x$

Step5: Isolate x terms

Subtract $5.90x$ from both sides:
$70 + 2.1x = 82.6$

Step6: Isolate constant terms

Subtract 70 from both sides:
$2.1x = 12.6$

Step7: Solve for x

Divide both sides by 2.1:
$x = \frac{12.6}{2.1} = 6$

Answer:

6 lb