SOLUTION: A snack food is made by mixing 4 lb of popcorn that costs $0.80 per pound with caramel that costs $2.90 per pound. how much caramel is needed to make a mixture that costs $1.70 per

Question 1173877: A snack food is made by mixing 4 lb of popcorn that costs $0.80 per pound with caramel that costs $2.90 per pound. how much caramel is needed to make a mixture that costs $1.70 per pound?
Found 3 solutions by josgarithmetic, ewatrrr, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
4 pounds at 0.8 per pound
plus
c pounds at $2.9 per pound
result to be
$1.7 per pound

Amount of resulting mixture is c+4 pounds.

Accounting for cost,

Simplify and solve for c.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi,
A snack food is made by mixing 4 lb of popcorn that costs $0.80 per pound with caramel that costs $2.90 per pound.
how much caramel is needed to make a mixture that costs $1.70 per pound?
Let x be the lbs of caramel needed.
Write as You read:
4(.80) + x(2.90) = (x+4)1.70
3.2 + (2.90)x = 1.70x +6.8
(1.20)x = 3.6
x = 3lb caramel is needed
Checking our Work:
3.20 + 8.70 = 11.90 = 7*1.70 checks.
Wish You the Best in your Studies.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is a non-algebraic method for solving this kind of two-part mixture problems that, with a little practice, can get you to the answer much faster and with less effort than setting up and solving an algebraic equation.

Look at the three prices per pound of the two ingredients and the mixture on a number line: 0.80, 1.70, and 2.90.
Determine by simple calculations that 1.70 is 0.90/2.10 = 3/7 of the way from 0.80 to 2.90.
That means 3/7 of the mixture is the $2.90 per pound caramels, so 4/7 is the $0.80 per pound popcorn.
And since the 4/7 of the mixture that is popcorn is 4 pounds, the 3/7 of the mixture that is caramels is 3 pounds.

ANSWER: 3 pounds of caramels

CHECK:
4(0.80)+3(2.90) = 3.20+8.70 = 11.90
7(1.70) = 11.90

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