Answer:
The intersection point is (2,2)
Step-by-step explanation:
First let's find the equation of f(x), using the linear model:
Using the point (0, 6), we have:
Using the point (3, 0), we have:
So we have that 
To find f'(x) (the inverse of f(x)), we can substitute f(x) by x and x by f'(x) in the equation of f(x) and then isolate f'(x):
Now, to find the intersection point, we need to calculate f(x) = f'(x):
And the y-value is:
So the point is (2,2)
Let's say a = number of ordered soups, b = number of ordered sandwiches.
Then 4.5a + 7.75b = 113.50, and a and b are integers between 0 and 18 inclusive.
How do we tackle this? If all ordered soup, the cost would be $81, so we'll have at least 4 sandwiches. If all ordered sandwich, the cost would be $139.5, so at most 15 sandwiches were ordered. You also know an even number of sandwiches was ordered, to let the price end at 50 cent.
If you brute-force from 4,6,8,10,12 to 14 sandwiches, you find the answer at 10 sandwiches and 8 soups.
10*7.75 + 8*4.50 = 113.50
G(x) = 2x² - 5x + 2 = 2x² - 4x - x + 2 = 2x · x - 2x · 2 - 1 · x - 1 · (-2)
= 2x(x - 2) -1(x - 2) = (x - 2)(2x - 1)
g(x) = 0 ⇔ (x - 2)(2x - 1) = 0 ⇔ x - 2 = 0 or 2x - 1 = 0
x = 2 or x = 0.5
