Solve the problem.
-An electronics company kept comparative statistics on two products, A and B. For the years 2003 to 2011, the total number of Product A ever sold (in thousands) is given by the equation y = 74x + 250, where x is the number of years since 2003. For that same period, the total number of Product B ever sold (in thousands) is given by the equation y = -30x + 434, where x is the number of years since 2003. Use the substitution method to solve the system and choose the statement that most accurately describes the solution.
A) At some point between 2003 and 2011, the company had sold 1800 of each product.
B) The company sold about 1.8 times as many of Product B as Product A.
C) When 383,000 of Product A had been sold, 1.8 times as many of Product B had been sold.
D) At about 1.8 years (to the nearest tenth) since 2003, the company sold the same number of Product A as Product B.

Question

Solve the problem.
-An electronics company kept comparative statistics on two products, A and B. For the years 2003 to 2011, the total number of Product A ever sold (in thousands) is given by the equation y = 74x + 250, where x is the number of years since 2003. For that same period, the total number of Product B ever sold (in thousands) is given by the equation y = -30x + 434, where x is the number of years since 2003. Use the substitution method to solve the system and choose the statement that most accurately describes the solution. 
A) At some point between 2003 and 2011, the company had sold 1800 of each product. 
B) The company sold about 1.8 times as many of Product B as Product A. 
C) When 383,000 of Product A had been sold, 1.8 times as many of Product B had been sold. 
D) At about 1.8 years (to the nearest tenth) since 2003, the company sold the same number of Product A as Product B.

Quizplus · Accepted Answer

To solve the system using substitution, we set the two equations equal to each other because we're looking for the point where the total sales of Product A equals the total sales of Product B: $74x + 250 = -30x + 434$. Solving for $x$ gives us the number of years since 2003 when the sales were equal. Solving the equation: $104x = 184$, we find $x = \frac{184}{104} \approx 1.77$, which rounds to about 1.8 years. This means around 1.8 years after 2003, the sales of both products were the same.

Solve the Problem. -An Electronics Company Kept Comparative Statistics on Two Products, a Two