Question

In order to raise money for holiday gifts for your family, you are planning on starting a dog walking and car wash business. You earn $12 per hour while dog walking and $18 per hour washing cars. You need to earn at least $600 during the month of November.
1.Assign a variable to represent the number of hours that you will spend dog walking in November. Write an expression to represent the amount of money you need to earn while dog walking.
2.Assign a variable to represent the number of hours that you will spend washing cars in November. Write an expression to represent the amount of money you need to earn while washing cars.
3.Write an algebraic model using inequalities that represents the total amount of money earned by dog walking and washing cars during the month of November.
4.Graph the algebraic model in the first quadrant only. Let the x-axis be the number of hours spent dog walking and the y-axis be the number of hours spent washing cars. Click here for a sheet of graph paper to print..
5.Use the graph and algebraic model to answer the following:
a.Why does the graph exist only in the first quadrant?
b.Are you able to earn exactly $600? Use the solutions of the system to find possible combinations of outcomes that equal exactly $600. Where do all of the combinations occur in the graph?
c.Is it possible to earn more than $600? Use the solutions of the system to find possible combinations of outcomes that are greater than $600. Where do all of the combinations occur in the graph?
d.If you work for 10 hours walking dogs and 10 hours washing cars, will you have earned enough money for the holiday gifts? Where does 10 hours walking dogs and 10 hours washing cars fall on the graph? Is this location representative of the solution to the algebraic model? Click here for a sheet of graph paper to print..
6.How would the algebraic model be different if you needed to earn more than $600? Adjust your algebraic model to show that you must earn more than $600. Would the graph of the model be different from the original? Would you include the line in the solution? What type of line represents "more than"? Graph your new algebraic model .
7.In complete sentences, explain the difference between a solid line and a dashed line when graphing an inequality. When graphing the two algebraic models, how did you determine which type of line to use?
8.How did you determine which part of the graph of the inequality to shade? What does the shaded area tell you? What does the area that is not shaded tell you?

Answer 1

#1. Let x be the number of hours spent dog walking, then the amount of money earned dog working is 12x.
#2. Let y be the number of hours spent washing cars, then the amount of money earned washing cars is 18y.
#3. $12x+18y \geq 600$