Question

Luke wants to mix dry roasted peanuts and dried cranberries to make a trail mix. He wants to make 20 ounces of trail mix and spend $11.

What weight of peanuts does he need to buy?

Answer 1

Using a system of equations, it is found that he needs to buy 0.75 pounds of peanuts.

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• For our system, we suppose that x is the weight of peanuts and y is the weight of cranberries.
• 20 ounces is equal to 1.25 pounds, thus:

$x + y = 1.25$

As we want x, we write y as a function of x, thus:

$y = 1.25 - x$

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• A pound of peanuts costs $8, and a pound of cranberries $10. In total, he wants to spend $11. Thus:

$8x + 10y = 11$

$8x + 10(1.25 - x) = 11$

$8x + 12.5 - 10x = 11$

$2x = 1.5$

$x = \frac{1.5}{2}$

$x = 0.75$

He needs to buy 0.75 pounds of peanuts.

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