Question

The finance department at a regional toy company has been tracking the income and costs of a new line of dolls. They have determined that the income and costs can be modeled by the equations below, where x is the number of dolls sold, in hundreds, and y is the total dollar amount, in thousands. Consider the system of equations that can be used to determine the number of dolls for which the company will break-even. How many total possible solutions of the form (x, y) are there for this situation? Of any possible solutions of the form (x, y), how many are viable for this situation?

a) 0 total solutions, 0 viable solutions
b) 1 total solution, 1 viable solution
c) 1 total solution, 0 viable solutions
d) 2 total solutions, 1 viable solution

Answer 1

The finance department at the regional toy company has determined that the income and costs of a new line of dolls can be modeled by the equations y = 3x - 2 and y = -4x + 6. There is 1 total solution and 1 viable solution for this situation.

Step-by-step explanation:

The finance department at the regional toy company has determined that the income and costs of a new line of dolls can be modeled by the equations y = 3x - 2 and y = -4x + 6. To find the number of dolls for which the company will break-even, we need to set the two equations equal to each other and solve for x:

3x - 2 = -4x + 6

7x = 8

x = 8/7

So, there is 1 total solution for this situation. To determine the number of viable solutions, we need to substitute the value of x back into one of the equations and solve for y:

y = 3(8/7) - 2

y = 34/7

Therefore, there is 1 viable solution for this situation.