Question

Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.

Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 1
February (2) 4 3
March (3) 5 5
April (4) 6 7

Answer 1

Based on the data provided in the table, we can see that f(x) represents the number of imports and g(x) represents the number of exports for each of the four months: January, February, March, and April.

To find the solution to the system of equations, we need to solve for x in both equations and then set them equal to each other. Doing so, we get:

f(x) = g(x)
3 + x = 1 + 2x
x = 2

Therefore, the solution to the system of equations is x = 2. This means that in the second month (February), the number of imports and exports were equal.

This solution represents the point at which the two lines representing f(x) and g(x) intersect. In other words, it is the point at which the number of imports and exports were equal. This point can be seen on the graph of the two functions as the point where the two lines intersect.

Overall, this information can be useful for decision-making and planning purposes, as it shows the point at which the imports and exports were balanced and can help inform future strategies for managing these two aspects of the business.