+1443 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)
+506 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:
\(\boxed{x=60, y=80}\)
