High School

Debra's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Debra $4.20 per pound, and type B coffee costs $5.90 per pound. This month, Debra made 139 pounds of the blend, for a total cost of $735.10.

How many pounds of type B coffee did she use?

Answer :

Debra used approximately 88.76 pounds of type B coffee.

Let [tex]x[/tex] be the number of pounds of type A coffee.
Let [tex]y[/tex] be the number of pounds of type B coffee.

  1. The total weight of the coffee blend is 139 pounds.
  2. The total cost of the coffee blend is $735.10.
  3. The cost per pound of type A coffee is $4.20.
  4. The cost per pound of type B coffee is $5.90.

From this, we can create the following equations:

  1. [tex]x + y = 139[/tex]
  2. [tex]4.20x + 5.90y = 735.10[/tex]

Now, we will solve this system of equations.

First, solve the first equation for [tex]x[/tex]:

[tex]x = 139 - y[/tex]

Next, substitute [tex]x[/tex] into the second equation:

[tex]4.20(139 - y) + 5.90y = 735.10[/tex]

Distribute the 4.20:

[tex]584.20 - 4.20y + 5.90y = 735.10[/tex]

Combine like terms:

[tex]584.20 + 1.70y = 735.10[/tex]

Subtract 584.20 from both sides:

[tex]1.70y = 150.90[/tex]

Divide both sides by 1.70 to isolate [tex]y[/tex]:

[tex]y = \frac{150.90}{1.70} \approx 88.76[/tex].

To check our solution, substitute [tex]y[/tex] back into the first equation to find [tex]x[/tex]:

[tex]x = 139 - 88.76 \approx 50.24[/tex]

Finally, verify the cost using both values:

[tex]4.20(50.24) + 5.90(88.76) = 210.98 + 523.68 \approx 734.66[/tex].

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