A coffee manufacturer wants to market a new blend of coffee that will sell for $3.90 per pound by mixing two coffees that sell for $2.75 per pound and $5 per pound, respectively. What amounts of each coffee should be blended to obtain 100 pounds of the desired mixture? Thanks so much if anyone can help me with this.

Question

A coffee manufacturer wants to market a new blend of coffee that will sell for $3.90 per pound by mixing two coffees that sell for $2.75 per pound and $5 per pound, respectively. What amounts of each coffee should be blended to obtain 100 pounds of the desired mixture? Thanks so much if anyone can help me with this.

Answer 1

x = lbs of cheaper coffee

2.75x = value of cheaper
100 - x = lbs of better coffee
5(100 - x) = value of better
100 = lbs of mixture
3.90(100) = value of mixture

2.75x + 5(100 - x) = 3.90(100)
Solve for x, lbs of cheaper
100 - x = lbs of better

Answer 2

To determine the amounts of each coffee that should be blended, we can set up a system of equations based on the given information.

Let's denote:
x = the amount (in pounds) of the $2.75 per pound coffee
y = the amount (in pounds) of the $5 per pound coffee

We have the following information:
1) The total weight of the mixture is 100 pounds: x + y = 100.
2) The cost of the mixture is $3.90 per pound: ($2.75 * x + $5 * y) / 100 = $3.90.

Now, let's solve the system of equations to find the values of x and y.

From the equation x + y = 100, we can solve for x in terms of y: x = 100 - y.

Substituting this value of x into the second equation, we get:
($2.75 * (100 - y) + $5 * y) / 100 = $3.90.

Simplifying this equation:
($275 - $2.75y + $5y) / 100 = $3.90.

Combining like terms:
($275 + $2.25y) / 100 = $3.90.

Multiplying both sides by 100 to eliminate the fraction:
$275 + $2.25y = $390.

Subtracting $275 from both sides:
$2.25y = $390 - $275.

Simplifying:
$2.25y = $115.

Dividing both sides by $2.25 to solve for y:
y = $115 / $2.25.

Calculating:
y ≈ 51.11 pounds.

Substituting this value of y into the equation x = 100 - y:
x = 100 - 51.11.

Calculating:
x ≈ 48.89 pounds.

Therefore, you should blend approximately 48.89 pounds of the $2.75 per pound coffee and 51.11 pounds of the $5 per pound coffee to obtain 100 pounds of the desired mixture.

Answer 3

To solve this problem, we can use a system of equations.

Let's assume x represents the amount of coffee costing $2.75 per pound, and y represents the amount of coffee costing $5 per pound.

The problem states that 100 pounds of the desired mixture will be produced, so we have the equation:

x + y = 100 ----(1)

The problem also states that the desired mixture will be sold for $3.90 per pound, so we have the equation:

(2.75x + 5y) / 100 = 3.90 ----(2)

Now, we can solve the system of equations (1) and (2) to find the values of x and y.

First, let's multiply equation (2) by 100 to remove the fraction:

2.75x + 5y = 390 ----(3)

Next, let's solve the system of equations (1) and (3) using either the substitution or elimination method.

Substitution method:

From equation (1), we can express x in terms of y:

x = 100 - y

Substituting this into equation (3):

2.75(100 - y) + 5y = 390
275 - 2.75y + 5y = 390
2.25y = 115
y = 51.11 (rounded to two decimal places)

Substituting this value of y back into equation (1):

x + 51.11 = 100
x = 48.89 (rounded to two decimal places)

Therefore, to obtain 100 pounds of the desired mixture, you should blend approximately 48.89 pounds of coffee costing $2.75 per pound and 51.11 pounds of coffee costing $5 per pound.