3.4+Planning+a+Skating+Party


 * PROBLEM 3.4, PLANNING A SKATING PARTY.

Your grade is planning a skating party. You are in charge of of renting the skates.

Roll-away skates price: $5 per person Wheelie's Skates and stuff price: 3$ per person plus 100 at the beginning.

Which company would you choose if you wanted to keep the costs to a minimum for your grade?

There are 60 students in my grade.

Y=$, X=People

Roll-away skates equation: X=60 Y=5x Y=5X60 Y=$300

Roll-away skates will cost $300 for all 60 students on our 7th grade.

Wheelie's Equation: X=60 Y=3x+100 Y=3X60+100 Y=$280 Wheelie's Skates only cost $280 for all 60 of our 7th grade students

I would choose Wheelie's Skates and stuff for our particular grade because it costs $20 less. I made my choice by plugging our x-value of 60 into both equations Y=5x and Y=3x+100 and then seeing which one cost less.

F.U.

1.

a. Write an equation for each company that can tell you how much each company will cost of any amount of people.

Roll-away skates: Y=5x Wheelie's skates: Y=3x+100

b. Graph the equations for both companies.



c. What range did you use for each value? How did you decide to use these ranges?

I went from 0-60 for the amount of people, and I went from 0-300 for the rental cost. I chose the range of people because that is how many people there are in my grade. I chose the range of rental cost because I knew what the highest and lowest costs were for each company.

2.

a. On which graph is the point (8,40)? What does this mean in terms of the cost to rent skates?

The point (8,40) is on the roll-away skates graph. This means that it will cost $40 for 8 people following the Roll-away skates plan.

b. On which graph is the point (8,124)? What does this point mean in terms of the cost to rent skates?

The point (8,124) is on the Wheelie's Skates graph. This means that it will cost $124 to pay for 8 people using the Wheelie's Skates plan.

c. Find the point of intersection on the two graphs, what does this point mean in terms of the cost to rent skates?

The point of intersection means that the costs are identical for both plans at that same point.

3.

a. Find the y-intercepts for the equations you graphed in question 1.

- The y-intercept for the Roll-away Skates equation is 0. - The y-intercept for the Wheelie's Skates equation is 100.

b. What do the y-intercepts mean in terms of the cost to rent skates? The y-intercept is the cost for 0 people using each plan.

c. How do the y-intercepts appear on the graph? The y-intercept is where the graph line starts for each plan.

d. Make tables for each plan. How do the y-intercepts appear in the tables?

Roll-away Skates table:

** Wheelie's skates table:
 * People || $ ||
 * 0 || 0 ||
 * 10 || 50 ||
 * 20 || 100 ||
 * 30 || 150 ||
 * 40 || 200 ||
 * 50 || 250 ||
 * 60 || 300 ||

The y-intercepts are the y-value when x is 0
 * People || $ ||
 * 0 || 100 ||
 * 10 || 130 ||
 * 20 || 160 ||
 * 30 || 190 ||
 * 40 || 220 ||
 * 50 || 250 ||
 * 60 || 280 ||

4. What are the coefficients of x in these equations? What do they mean in terms of the cost to rent skates? What effect to the coefficients have on the graph?

The coefficient of x in the roll-away skates plan is 5. In the Wheelie's skates plan, the coefficient of x is 3. The coefficient are what x is multiplied by to find the value of y. The coefficient determines the steepness of the slope.

5. Which company would you choose if 100 students were attending the party? Why?

I would choose Wheelie's skates because it costs less even though it starts at $100, it only costs $400 and Roll-away costs $500 for 100 people.

6. If you can only spend $250 on skates, how many pairs can you rent from each company?

You can buy 50 skates from each company with $250.