Keil is going to make 13 pounds of mixed nuts for a party, Peanuts cost $3.00 per pound and fancy nuts cost $6.00 per pound. If Keil can spend $63.00 on nuts, how many pounds of each should he buy?

1 Answer
Nov 9, 2016

Answer:

This is a really neat way of calculating properties of blends.

Need to purchase 8lb fancy nuts and 5lb peanuts

Explanation:

If the weight is always going to be 13 lb then you only need to look at one of the blended items as the other's quantity is directly related.

For example: Suppose I chose to have 12lb of the fancy nuts then the amount of peanuts is 13-12=1

Thus we can use the following graph.
Tony B

If the blend is all fancy nuts then then there are no peanuts so the total cost is that of 13 lb of fancy nuts. #13xx$6=$78#

If the blend is all peanuts then there are no fancy nuts so the cost is that of 13 lb of peanuts. #13xx$3=$39#

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The gradient of part of the line is the same as the gradient of all of the line. So we have:

#" "(13 lb)/($78-$39) = (xlb)/($63-$39)#

#" "xlb= (13(63-39))/(78-39) =8lb#
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Need to purchase 8lb fancy nuts and 5lb peanuts

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#color(blue)("Check")#

#8lb xx $6.00 = $48.00#
#5lb xx $3.00 =ul($15.00) larr" Add"#
#" "$63.00 larr" As required"#