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Solve by elimination.

 

Rachel has started a small company making organic honey. She makes large and small containers. She has found the costs of running her business to have a linear relationship which can be 5.5x + 7.5y = 930. She wants to sell a small container for 12 dollars and a larger container for 15 dollars and earn 1920 dollars. That creates a linear relationship modeled by 12x + 15y = 1920. How many of each kind of organic honey containers should she sell to fulfill her revenue and cost projections? (Hint: 7.5 * -2 = -15)

 Jan 15, 2021
 #1
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Using the hint at the very end, we can multiply \(5.5x+7.5y=930\) by -2 to make it easier:

\(-11x-15y=-1860\\ 12x+15y=1920\)

Add the equations together to cancel out the y term:

\(x=60\)

Now that we know x, we can plug x back into any of the 2 equations above to solve for y (I chose the second one because it seems simpler):

\(12(60)+15y=1920\\ 720+15y=1920\\ 15y=1200\\ y=80\)

Therefore, the answer is:

\(\boxed{x=60, y=80}\)

 Jan 16, 2021

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