Answer: Let's use a graphical method to solve the system of equations to determine the number of small cups sold (x) and large cups sold (y).
We have two equations based on the given information:
The total number of ounces sold is 800:
10x + 20y = 800
He sold twice as many small cups as large cups:
x = 2y
To graphically solve this system of equations, we'll plot both equations on the same graph and find their point of intersection, which represents the solution (x, y) for the number of small and large cups sold.
Step 1: Plot the equations on a graph.
For the equation 10x + 20y = 800, let's rearrange it to solve for y:
20y = 800 - 10x
y = (800 - 10x) / 20
y = 40 - 0.5x
For the equation x = 2y, we can write it as y = x/2.
Now, we can plot both equations on the graph:
Step 2: Graph the equations.
The graph of y = 40 - 0.5x is a straight line with a y-intercept of 40 and a slope of -0.5 (it goes downward from left to right). The graph of y = x/2 is also a straight line with a y-intercept of 0 and a slope of 1/2 (it goes upward from left to right).
Step 3: Find the point of intersection.
The solution (x, y) will be the point where the two lines intersect. By visually inspecting the graph, we can find the point of intersection:
Graphically, the point of intersection appears to be approximately (x, y) ≈ (20, 10).
Step 4: Interpret the results.
According to the graph, it appears that the number of small cups sold (x) is approximately 20, and the number of large cups sold (y) is approximately 10. However, this is only an approximation from the graph.
Keep in mind that graphical solutions are not always precise, and if you need exact values, it's better to use algebraic methods like substitution or elimination to solve the system of equations.