a coffee company wants a new flavor of cajun coffee. how many pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $3 a pound to get mixture worth $6 a pound
amount to be added --- x lbs
10x + 3(20) = 6(x+20)
10x + 60 = 6x + 120
4x = 60
x = 15
To find out how many pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $3 a pound to get a mixture worth $6 a pound, we can use the concept of weighted averages.
Let's assume that x pounds of coffee worth $10 a pound should be added.
To solve this problem, follow these steps:
Step 1: Calculate the total cost of the first type of coffee.
20 pounds of coffee worth $3 a pound can be calculated as:
20 * $3 = $60
Step 2: Calculate the total cost of the second type of coffee.
x pounds of coffee worth $10 a pound can be calculated as:
x * $10 = $10x
Step 3: Calculate the total cost of the final mixture.
The final mixture has a total weight of (20 + x) pounds, worth $6 a pound. So, its total cost can be calculated as:
(20 + x) * $6 = $6(20 + x)
Step 4: Set up the equation using the weighted average principle.
According to the weighted average principle, the total cost of the first type of coffee plus the total cost of the second type of coffee should equal the total cost of the final mixture.
$60 + $10x = $6(20 + x)
Step 5: Solve the equation for x.
Simplify the equation:
$60 + $10x = $120 + $6x
Combine like terms:
$10x - $6x = $120 - $60
$4x = $60
Divide both sides of the equation by $4:
x = $60 / $4
x = 15
Answer:
Therefore, 15 pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $3 a pound to get a mixture worth $6 a pound.
To find out how many pounds of coffee worth $10 per pound should be added to 20 pounds of coffee worth $3 per pound to get a mixture worth $6 per pound, you can use the method of weighted averages.
Let's assume that x pounds of coffee worth $10 per pound need to be added.
To calculate the weighted average, you need to consider two components: the pounds of coffee and their corresponding values.
For the first component, you have 20 pounds of coffee worth $3 per pound. This can be represented as:
20 pounds * $3/pound = $<<20*3=60>>60
For the second component, you have x pounds of coffee worth $10 per pound. This can be represented as:
x pounds * $10/pound = $10x
Now, for the total mixture, you have (20 + x) pounds of coffee worth $6 per pound. This can be represented as:
(20 + x) pounds * $6/pound = $6(20 + x) = $<<6*(20+x)=120+6x>>120 + $6x
Since the final mixture needs to have an average value of $6 per pound, the two components must add up to an equal value. Therefore, we can set up the equation:
$60 + $10x = $120 + $6x
To isolate x, we can rearrange the equation:
$10x - $6x = $120 - $60
$4x = $60
Dividing both sides by $4, we get:
x = $60 / $4
x = 15 pounds
So, to obtain a mixture worth $6 per pound, you would need to add 15 pounds of coffee worth $10 per pound to the 20 pounds of coffee worth $3 per pound.