A store manager wishes to reduce the price of her fresh ground coffee by mixing two grades. If she has 50 pounds of coffee which sells for $1.20 per pound, how much coffee worth 80 cents per pound must she mix with it so that she can sell the final mixture for $1.00 per pound?
assume C and E types, which represent lbs of each.
C=50
50*1.20+.80E=1.00*(50+E)
60+.8E=50+E
.2E=10
E=50 lbs
To find out how much coffee worth 80 cents per pound the store manager must mix with the 50 pounds of coffee worth $1.20 per pound, we can use the weighted average formula.
Let's assume the store manager needs to mix x pounds of coffee worth 80 cents per pound.
The total value of the 50 pounds of $1.20 coffee can be calculated as:
50 * $1.20 = $60
The total value of x pounds of 80 cent coffee can be calculated as:
x * $0.80 = $0.80x
The total value of the final mixture, when sold for $1.00 per pound, can be calculated as:
(50 + x) * $1.00 = $1.00(50 + x) = $50 + $1.00x = $50 + x
Since the total value of the final mixture is equal to the sum of the individual values, we can set up the equation:
$60 + $0.80x = $50 + x
Now, let's solve for x:
$0.80x - x = $50 - $60
-0.20x = -$10
x = -$10 / -0.20
x = 50
Therefore, the store manager must mix 50 pounds of coffee worth 80 cents per pound with the 50 pounds of coffee worth $1.20 per pound in order to sell the final mixture for $1.00 per pound.
To find out how much coffee worth 80 cents per pound the store manager needs to mix, we can set up an equation based on the given information.
Let's assume the amount of coffee worth 80 cents per pound that needs to be mixed is x pounds.
The cost of the coffee worth $1.20 per pound is 50 pounds for $1.20/pound, which can be written as:
50 * $1.20 = $60
The cost of the coffee worth 80 cents per pound (x pounds) can be calculated as:
x * $0.80 = $0.80x
The total cost of the final mixture is $1.00 per pound, which can be calculated as:
(50 + x) * $1.00 = $1.00(50 + x)
Now, based on the given information, we can set up the equation:
$60 + $0.80x = $1.00(50 + x)
Simplifying the equation:
$60 + $0.80x = $50 + $1.00x
To isolate x, we need to move all terms with x to one side:
$0.80x - $1.00x = $50 - $60
-$0.20x = -$10
Dividing both sides of the equation by -0.20 to solve for x:
x = $10 / -0.20
x = -50
The negative value for x doesn't make sense in this context, so we can ignore it. This means there is no need to mix in any coffee worth 80 cents per pound. The store manager can reduce the price of her fresh ground coffee by simply selling it for $1.20 per pound.