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42 votes
While scouring the frozen tundra of the North Pole looking for Rudolph, Clarice spots a snow storm approaching at a distance. Hastily, she decides to take shelter in the closest cave she could find. Unknowingly, she walks into the home of the Bumble. Caught between a snow storm and the Bumble, she decides to hide behind a group of stalagmites. Clarice notices the Bumble creating tree toppers for Christmas trees off at a distance. If the Bumble can make 43 tree toppers per hour and he works 12 hours a day, spending the other 12 hours to forage for food, sleep, and terrify the locals, how many tree toppers can he make by Christmas Eve if he begins working December 1st? Write and graph an equation to represent the number of tree toppers made by the Bumble at any given point in the month of December before Christmas Eve. Sketch a picture and show all your work

User BillyTom
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1 Answer

24 votes
24 votes

The situation shows two variables;

The number of days in the month (x variable) and the number of tree toppers made per day (y variable).

The Bumble can make 43 tree toppers every hour. If he works for 12 hours daily, that means he can make

Per day = 43 x 12

per day = 516 tree toppers

This means for the second day, he would have made, 516 x 2 = 1032 tree toppers. The equation to depict is derived as follows;


\begin{gathered} y=mx+b \\ \text{Identify two points as} \\ A(1,516),B(2,1032) \\ m=(y2-y1)/(x2-x1) \\ m=(1032-516)/(2-1) \\ m=(516)/(1) \\ m=516 \\ \text{Inputing the values of x and y into the equation, we now have b as;} \\ y=mx+b \\ 516=516(1)+b \\ 516=516+b \\ 516-516=b \\ b=0 \\ \text{Hence, the equation is shown as;} \\ y=mx+b \\ y=516x+0 \\ y=516x \end{gathered}

This means for every value of x (that is for every subsequent day after december 1st), the value of y (number of tree toppers) can be derived from the equation shown above. Hence, we can write out an ordered pair as follows;


(1,516),(2,1032),(3,1548),(4,2064)\ldots

In the same manner we can now write out the entire ordered pair from December 1 to december 24, and then the graph can be drawn as shown below;

While scouring the frozen tundra of the North Pole looking for Rudolph, Clarice spots-example-1
User RQube
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