Mixture Problems Template – Price Problems

Copy the problem from the lesson:
1. A store manager wishes to reduce the price on her fresh ground coffee by mixing two grades. If she has 50 pounds of coffee which sells for $10 per pound, how much coffee worth $6 per pound must she mix with it so that she can sell the final mixture for $ 8.50 per pound?

What Do I Know?
She has 50 lbs. @ $10 per pound
She needs ??? @ $6 per pound
The mixture will sell for $8.50 per pound

What Do I Want to Know?
how many pounds of coffee @ $6 per pounds

Assign Variables
Let B = pounds of better grade of coffee
Let L = pounds of lower grade of coffee
Let T = total pounds of coffee after mixing

Write a verbal Model:
Pounds of lower grade coffee + 50 lbs. of better grade coffee = total pounds of coffee.

How Do I Find the Components of the Verbal Model?

Write an Algebraic Equation

Solve

Write Your Summary Statement

There is no need to have all those variables, since there is only one, the amount of lower grade coffee defined by L

my equation would be
10(50) + 6L = 8.5(50+L)

and I got L = 30

To solve this price mixture problem, we can follow these steps:

1. First, let's assign variables to the quantities we want to find. Let B represent the pounds of the better grade coffee and L represent the pounds of the lower grade coffee.

2. From the problem, we know that the store manager has 50 pounds of coffee that sells for $10 per pound. So the value of the better grade coffee is 50 * $10 = $500.

3. We also know that the store manager wants to mix this coffee with some coffee worth $6 per pound so that the final mixture sells for $8.50 per pound.

4. To find the pounds of the lower grade coffee (L), we need to set up an equation based on the verbal model: Pounds of lower grade coffee + 50 lbs. of better grade coffee = total pounds of coffee.

5. Since we want to sell the final mixture for $8.50 per pound, the total value of the mixture will be T * $8.50.

6. The total value of the mixture is the sum of the individual values of the better grade coffee and the lower grade coffee. So we can write the equation as follows:

Value of better grade coffee + Value of lower grade coffee = Total value of mixture.
$500 + (L * $6) = (50 + L) * $8.50

7. Simplify the equation by multiplying the terms:
$500 + 6L = 50 * $8.50 + L * $8.50

8. We can then expand and solve for L:
$500 + 6L = $425 + 8.5L
2.5L = $75
L = $75 / 2.5
L = 30 pounds of lower grade coffee

Therefore, the manager needs to mix 30 pounds of coffee worth $6 per pound in order to sell the final mixture for $8.50 per pound.