Question

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?

Answer 1

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.

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"`