Question

Suppose that a salesperson observes that if an item is priced at $7 per item then 12 items are sold. If 10 items are sold for $9 per item then find an equation to model the number y of items sold for x dollars per item.

Answer 1

To find the equation that models the number of items sold, we can set up a system of equations using the given information. Solving the system of equations, the equation that models the number of items sold for x dollars per item is y = -2x + 26.

Step-by-step explanation:

In order to find the equation that models the number of items sold, we can use the given information and set up a system of equations.

From the first piece of information, we know that when the price is $7 per item, 12 items are sold. This can be represented as the equation x = 7, y = 12, where x is the price per item and y is the number of items sold.

From the second piece of information, we know that when 10 items are sold for $9 per item. This can be represented as the equation x = 9, y = 10.

By setting up the system of equations, we can solve for the equation that models the number of items sold for x dollars per item. The system of equations is:

7 = x, 12 = y

9 = x, 10 = y

Solving this system of equations, we find that the equation to model the number of items sold for x dollars per item is y = -2x + 26.