SOLUTION: A snack mix is made from peanuts that cost $3.10 per pound and caramel popcorn that cost $2.30 per pound. The mixture costs $2.80 per pound. Does the mixture contain more peanuts o

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Question 1017220: A snack mix is made from peanuts that cost $3.10 per pound and caramel popcorn that cost $2.30 per pound. The mixture costs $2.80 per pound. Does the mixture contain more peanuts or more popcorn?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i would say more peanuts than caramel popcorn.

here's why:

let c = number of pounds of caramel popcorn
let p = number of pounds of peanuts

peanuts costs 3.10 per pound.
total cost of peanuts is therefore 3.10 * p

caramel popcorn costs 2.30 per pound.
total cost of caramel popcorn is therefore 2.30 * c

your formula is 3.10 * p + 2.30 * c = 2.80 * (p + c)

simplify by distributing the multiplication on the right side of the equation to get 3.10 * p + 2.30 * c = 2.80 * p + 2.80 * c

subtract 2.80 * p from both sides of the equation and subtract 2.30 * c from both sides of the equation to get 3.10 * p - 2.80 * p = 2.80 * c - 2.30 * c

simplify to get .30 * p = .50 * c

divide both sides of the equation by .30 to get p = (.50 / .30) * c = 5/3 * c.

this means that p > c

let's see if that's true.

assume c = 3 pounds.

this makes p = 5/3 * 3 = 5 pounds.

original formula says:

3.10 * p + 2.30 * c = 2.80 * (p + c)

since p = 5 and c = 3, this formula becomes:

3.10 * 5 + 2.30 * 3 = 2.80 * 8

solve to get:

22.4 = 22.4

solution looks good.

the mixture contains more peanuts than caramel popcorn.