A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound?
amount of the good stuff to be added ---- x pounds
then....
10x + 4(30) = 5(30+x)
solve for x
A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound?
To find the number of pounds of coffee worth $10 a pound that should be added, we need to set up an equation based on the given information. Here's how you can do it step by step:
Let's assume the number of pounds of coffee worth $10 a pound to be added is "x".
Step 1: Determine the total cost of the coffee worth $10 a pound. Since the cost is given as $10 per pound and the number of pounds is "x", the total cost would be 10x dollars.
Step 2: Determine the total cost of the coffee already available. We are given that there are 30 pounds of coffee worth $4 a pound. Hence, the total cost of this coffee would be 4 * 30 = 120 dollars.
Step 3: Determine the total amount of coffee (in pounds) in the mixture. It will be the sum of the coffee already available (30 pounds) and the coffee to be added (x pounds). So, the total amount of coffee in pounds is x + 30.
Step 4: Since we want the mixture to have a value of $5 a pound, the total cost of the mixture should be 5 times the total amount of coffee in pounds. In equation form, this is 5 * (x + 30).
Step 5: Set up the equation by equating the total cost of the mixture (5 * (x + 30)) to the sum of the individual costs (10x + 120):
5(x + 30) = 10x + 120
Step 6: Solve the equation:
5x + 150 = 10x + 120
5x - 10x = 120 - 150
-5x = -30
x = -30 / (-5)
x = 6
Therefore, 6 pounds of coffee worth $10 a pound should be added to the mixture.