Percentage problems
Caramels costing $3.75 per pound are mixed with chocolates costing $3 per pound to make a 6 pound mixture that will be sold at $3.25 per pound. How many pounds of each are needed?
3.75x + 3y = 3.25
x + y = 1
x = 1 - y
3.75x + 3y = 3.25
3.75(1 - y) + 3y = 3.25
3.75 - 3.75y + 3y = 3.25
-0.75y = -0.5
y = 0.666 = 2/3
x + 2/3 = 1
x = 1/3
To make 1 lb of the mixture requires 1/3 lb of the caramels and 2/3 lb of the chocolates.
To make 6 lbs of the mixture requirs 6 * 1/3 lb = 2 lbs of the caramels and 6 * 2/3 lb = 4 lbs of the chocolates.
Check.
3.75x + 3y = 3.25
3.75(1/3) + 3(2/3) = 3.25
1.25 + 2 = 3.25
Answer: 2 lbs of the caramels, 4 lbs of the chocolates to make 6 lbs of the mixture