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A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $9.40 per pound with a Gualtemala Antigua coffee blend that normally sells for $12.90 per pound to create 50 pounds of a coffee that can sell for $12.34 per pound. How many pounds of each kind of coffee should they mix?

A) Write an equation using the information as it is given above that can be solved to answer the question. Use
x
as your variable to represent the quantity of Organic Free Trade coffee blend.
Equation:


B) Answer: They must mix
pounds of the Organic Free Trade Blend
pounds of the Gualtemala Antigua Blend.
Round your answers to the nearest whole number of pounds.
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Answer :

MrRoyal

The mix of the coffee blends is an illustration of a linear equation.

  • The equation that represents the scenario is [tex]9.40x + 12.90y = 617[/tex].
  • 8 pounds of Organic Free Trade coffee blend and 42 blends of Gualtemala Antigua coffee blend should be mixed.

Let:

[tex]x \to[/tex] Organic Free Trade coffee blend

[tex]y \to[/tex] Gualtemala Antigua coffee blend

A. The equation

To create 50 pounds, we have:

[tex]x + y = 50[/tex]

The equation is generated by multiplying the unit rates by the pound of each coffee blend.

So, the equation is:

[tex]9.40 \times x + 12.90 \times y = 12.34 \times 50[/tex]

[tex]9.40x + 12.90y = 617[/tex]

B. The quantity of each

We have: [tex]x + y = 50[/tex]

Make x the subject

[tex]x = 50 - y[/tex]

Substitute [tex]x = 50 - y[/tex] in [tex]9.40x + 12.90y = 617[/tex]

[tex]9.40 \times (50 - y) + 12.90y = 617[/tex]

Open brackets

[tex]470 - 9.40y + 12.90y = 617[/tex]

Collect like terms

[tex]- 9.40y + 12.90y = 617 - 470[/tex]

[tex]3.5y = 147[/tex]

Solve for y

[tex]y = \frac{147}{3.5}[/tex]

[tex]y = 42[/tex]

Substitute [tex]y = 42[/tex] in [tex]x = 50 - y[/tex]

[tex]x = 50 - 42[/tex]

[tex]x = 8[/tex]

Hence, they must mix 8 pounds of Organic Free Trade coffee blend and 42 blends of Gualtemala Antigua coffee blend

Read more about linear equations at:

https://brainly.com/question/13473963

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