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Sagot :
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:
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