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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?

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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:

  • [tex]G = 20 - C[/tex]

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

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

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

  • [tex]G + 5 = 20\\G = 20 - 5\\G = 15[/tex]

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

marvineetesh3

Ratios is the quantitative relation between two magnitudes, presenting the number of times one value comprises within the other.

The total pounds of the gourmet brand and  cheaper brand that should be mixed in the ratio of $15 pounds and $5 ponds.

What is the ratio?

In mathematics, a ratio shows how many times one number contains another.

For example:

If there are 12 pencils and 6 scales in a compass of a student, then the ratio of pencils to scales is 12:6.

Computation mixed price of both the coffee:

Given,

Price of gourmet coffee = $9.00/- pound,

Price of cheaper coffee = $7.00/- pound.

Let x be the number of pounds of the gourmet brand of coffee that should be mixed.

Let (20-x) the number of pounds of the cheaper brand of coffee that should be mixed.

Then,

[tex]9(x) + \$7(20-x) = 20\times\$8.5\\\\9x+\$140-7x=\$170\\\\2x+\$140=\$170\\\\x=15[/tex]

Now, put the value of x (gourmet brand of coffee)  = $15, and

The values of (20-x) means cheaper brand of coffee= 20-$15= $5.

Therefore, The total pounds of the gourmet brand and cheaper brand that should be mixed in the ratio of  $15 pounds and $5 ponds to achieve the target of 20 pounds.

Learn more about the ratios, refer to:

https://brainly.com/question/1504221

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