Question

A company manufactures and sells mini-recorders. A survey of office supply stores indicated that at a price of 71 each, the demand would be two hundred recorders, and at a price of 31 each, the demand would be seven hundred recorders. If a linear relationship between price and demand exists, which of the following equations models the price-demand relationship?

1) y = 5x + 100
2) y = 10x + 100
3) y = 5x + 200
4) y = 10x + 200

Answer 1

The price-demand relationship can be represented by the equation y = mx + b. By using the given data points, we can solve a system of equations to find the values of m and b, which will help us determine the correct equation for the price-demand relationship. In this case, none of the provided options match the correct equation.

Step-by-step explanation:

The price-demand relationship can be represented by an equation of the form y = mx + b, where y represents the price and x represents the demand. We can use the given information to find the slope (m) and y-intercept (b) values. At a price of $71, the demand is 200 recorders, so we can write the equation 71 = 200m + b. Similarly, at a price of $31, the demand is 700 recorders, so we can write the equation 31 = 700m + b. We can then solve this system of equations to find the values of m and b, which will help us determine the correct equation for the price-demand relationship.

To solve the system of equations, we can subtract the second equation from the first equation to eliminate b: (71 - 31) = (200m + b) - (700m + b). Simplifying, we get 40 = -500m. Dividing both sides by -500, we find that m = -0.08. Plugging this value of m back into one of the original equations, we can solve for b: 71 = 200(-0.08) + b. Simplifying, we get b = 88.

Therefore, the correct equation that models the price-demand relationship is y = -0.08x + 88. Out of the given options, none of them match this equation. Therefore, the correct answer is none of the provided equations.