How much coffee that is $10 per pound should be added to 30 pounds of coffee at $3 per pound to get a coffee $5 per pound?
Tendollarlbs*10+30*3=(30+tenndollarlbs)5
solve for tendollarlbs
To solve this problem, we need to find out how much coffee that costs $10 per pound should be added to the existing 30 pounds of coffee that costs $3 per pound in order to obtain a mixture that costs $5 per pound.
Let's denote the amount of coffee that costs $10 per pound as "x".
To determine the answer, we can use the concept of weighted averages. The weighted average of a mixture is calculated by taking the sum of the products of the quantities and their respective weights, divided by the sum of the weights.
In this case, the weighted average is $5 per pound. We can set up the following equation:
(30 * $3 + x * $10) / (30 + x) = $5
This equation represents the average price of the mixture, where $3 is the price per pound of the existing 30 pounds of coffee, $10 is the price per pound of the coffee to be added, and $5 is the target average price.
To solve the equation, we can cross-multiply:
30 * $3 + x * $10 = (30 + x) * $5
Simplifying the equation:
90 + 10x = 150 + 5x
Rearranging the terms:
10x - 5x = 150 - 90
5x = 60
Dividing both sides by 5:
x = 12
Therefore, you would need to add 12 pounds of coffee that costs $10 per pound to the existing 30 pounds of coffee at $3 per pound to obtain a mixture that costs $5 per pound.