Question 1178461: The table shows the sales of two companies for the year 2000 and the targeted sales after 10 years.
Company
Sales in 2000 (millions of AFN)
Sales target for 2010 in (millions of AFN)
A
2.00
2.60
B
2.70
3.10
Let x represent the number of years since 2000 and y represent sales in millions of AFN.
Write the system of equations to represent the sales of the two companies.
Solve the system using the elimination method and interpret the solution.
Show all your steps
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely! Let's break down this problem step-by-step.
**1. Setting up the Equations**
We're given two data points for each company:
* **Company A:**
* (0, 2.00) - Sales in 2000
* (10, 2.60) - Sales target in 2010
* **Company B:**
* (0, 2.70) - Sales in 2000
* (10, 3.10) - Sales target in 2010
We'll assume a linear growth model for simplicity, so we'll use the slope-intercept form (y = mx + b).
* **Company A:**
* Slope (m): (2.60 - 2.00) / (10 - 0) = 0.60 / 10 = 0.06
* Y-intercept (b): 2.00 (sales in 2000)
* Equation: y = 0.06x + 2.00
* **Company B:**
* Slope (m): (3.10 - 2.70) / (10 - 0) = 0.40 / 10 = 0.04
* Y-intercept (b): 2.70 (sales in 2000)
* Equation: y = 0.04x + 2.70
Therefore, the system of equations is:
* y = 0.06x + 2.00 (Company A)
* y = 0.04x + 2.70 (Company B)
**2. Solving the System Using the Elimination Method**
Since both equations are already solved for y, we can use substitution or a modified elimination method. We will use substitution here.
Since both equations equal y, we set the right sides of the equations equal to each other.
0.06x + 2.00 = 0.04x + 2.70
Now, solve for x:
* 0.06x - 0.04x = 2.70 - 2.00
* 0.02x = 0.70
* x = 0.70 / 0.02
* x = 35
Now, substitute x = 35 into either equation to find y. Let's use the equation for Company A:
* y = 0.06(35) + 2.00
* y = 2.10 + 2.00
* y = 4.10
Therefore, the solution is x = 35 and y = 4.10.
**3. Interpreting the Solution**
* x = 35 means that 35 years after 2000, which is the year 2035.
* y = 4.10 means that the sales for both companies will be 4.10 million AFN.
**Interpretation:**
In the year 2035, the sales of both Company A and Company B are projected to be equal, at 4.10 million AFN.
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