How many pounds of each should I buy if I have $15.00 and wish to buy five pounds of mixed nuts for a party where peanuts cost $2.20 per pound and cashews cost $4.70 per pound?

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Answer 1 · 2014-11-04T16:02:23

Let $p$ be the amount of peanuts
Let $c$ be the amount of cashews

Since we only need 5 pounds of nuts,
$p + c = 5$
$=> p = 5 - c$

$2.20(p) + 4.70(c) = 15.00$

$=> 2.20(5 - c) + 4.70(c) = 15.00$

$=> 2.20(5) + 2.20(-c) + 4.70c = 15.00$

$=> 11.00 - 2.20c + 4.70c = 15.00$

$=> 2.50c = 4$

$=> c = 1.6$

$p = 5 - c$

$=> p = 5 - 1.6$

$=> p = 3.4$

You should buy 1.6 lbs of cashews and 3.4 pounds of peanuts