The manager has one type of coffee that sells for $5 per pound and another type that sells for $11 per pound. The manager wishes to mix 90 pounds of the $11 coffee to get a mixture that will sell for $10 per pound. How many pounds of $5 coffee should be used?

To solve this problem, we can use the concept of weighted averages. Here's how we can approach it:

Let's assume that the manager needs to mix x pounds of the $5 coffee.

Step 1: Calculate the total cost of the mixture
The total cost of the mixture is the sum of the individual costs of the two types of coffee.

For the $11 coffee:
The manager wants to mix 90 pounds of the $11 coffee. Therefore, the cost of the $11 coffee is:
90 pounds * $11/pound = $990

For the $5 coffee:
The manager wants to mix x pounds of the $5 coffee. Therefore, the cost of the $5 coffee is:
x pounds * $5/pound = $5x

The total cost of the mixture is the sum of the cost of each type of coffee:
$990 + $5x

Step 2: Calculate the total weight of the mixture
The total weight of the mixture is the sum of the weights of the two types of coffee.

For the $11 coffee:
The manager wants to mix 90 pounds of the $11 coffee. Therefore, the weight of the $11 coffee is:
90 pounds

For the $5 coffee:
The manager wants to mix x pounds of the $5 coffee. Therefore, the weight of the $5 coffee is:
x pounds

The total weight of the mixture is the sum of the weight of each type of coffee:
90 pounds + x pounds

Step 3: Set up the equation
The average price per pound of the mixture is given as $10. Using the formula for average (sum of values divided by the total number of values), we can set up the equation:

Average price per pound = Total cost of mixture / Total weight of mixture

$10 = ($990 + $5x) / (90 pounds + x pounds)

Step 4: Solve the equation
To solve the equation, we can cross-multiply and simplify:

10(90 + x) = 990 + 5x
900 + 10x = 990 + 5x
10x - 5x = 990 - 900
5x = 90
x = 90 / 5
x = 18

Therefore, the manager should use 18 pounds of the $5 coffee to mix with the 90 pounds of the $11 coffee to get a mixture that will sell for $10 per pound.

Let's assume the amount of $5 coffee to be used is x pounds.

Since the manager wishes to mix 90 pounds of the $11 coffee to get a mixture that will sell for $10 per pound, the total weight of the mixture will be 90 pounds.

So, the weight of the $11 coffee used is 90 pounds.

Now, let's find the weight of the $5 coffee used.

The average price of the mixture will be the weighted average of the prices of the two types of coffee used.

10 = (11 * 90 + 5 * x) / (90 + x)

Multiplying both sides of the equation by (90 + x):

10(90 + x) = 11(90) + 5x

900 + 10x = 990 + 5x

Simplifying the equation:

10x - 5x = 990 - 900

5x = 90

Dividing both sides of the equation by 5:

x = 18

Therefore, the manager should use 18 pounds of $5 coffee.

let the number of pounds of the cheaper kind be x

solve for x

11(90) + 5x = 10(90+x)