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Kazeer [188]
3 years ago
9

A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually sells for ​$9.00 per pound

. The cheaper brand sells for ​$7.00 per pound. How much of each type should be mixed in order to have 20 pounds of coffee that is worth ​$8.50 per​ pound?
Business
1 answer:
AleksandrR [38]3 years ago
3 0

Answer:

15lbs of gourmet coffee and 5lbs of cheap coffee.

Explanation:

To solve this problem, we will use the substitution method. Step by step explanation:

1. Defining the variables:

  • G: For gourmet coffee
  • C: For cheap coffee

2. Setting up the equations:

We need to find a combination of G and C that will result in 20 pounds worth $8.50 per lbs. As such, we have:

  1. G + C = 20lbs
  2. $9.00G + $7.00C = $8.50/lbs x 20lbs

3. Solving equation 1 for any of the variables. We will go with variable G:

  • G = 20 - C

4. Substituting variable G in equation 2 to find C:

  • 9(20 - C) + 7C = 8.5 * 20\\180 - 9C + 7C = 170\\180 - 170 = 9C - 7C\\10 = 2C\\\frac{10}{2}=C\\C = 5

5. Substituting variable C in equation 1 to find the value of G:

  • G + 5 = 20\\G = 20 - 5\\G = 15

Then, we need <em>15lbs</em> of gourmet coffee and <em>5lbs</em> of cheap coffee to have <em>20lbs</em> of coffee worth <em>$8.50/lbs.</em>

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