I am trying to make my own Chex Party Mix and sell at a Fund Raiser for Underpai

Question

I am trying to make my own Chex Party Mix and sell at a Fund Raiser for Underpaid College Professors. I would like to create 100 pounds of mix that would have an average cost of $1.60 per pound. I will be using the following ingredients: Chex Cereal - 90 cents per pound Planters Peanuts - $4.25 per pound Roll Gold Pretzels - $2.75 per pound In my mix, for each pound of peanuts, I would use 2 pounds of Pretzels. How many pounds of Chex Cereal will I need to use to have 100 pounds of mix with an average cost of $1.60 per pound

Explanation / Answer

Mix's average cost = $1.60 per pound

So, for 100 pounds,

cost = 1.60*100

= 160 $

x + y + 2y = 100

=> x + 3y = 100

0.9x + 4.25y + 2.75(2y) = 160

=> 0.9x + (4.25 + 5.5)y = 160

=> 0.9x + 9.75y = 160

On solving, we get

x = 70.21

70.21 pounds of Chex Cereal will be used.

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