Question

Mrs. Claus is helping prepare Santa for his Christmas Eve journey around the world. If his belly is to shake like a bowl full of jelly when he laughs, Santa will need to gain 4 and a quarter pounds of weight each day beginning December 1st. What will Santa’s weight be on December 24th if his initial weight is 185 pounds? Write and graph a linear function to represent his weight at any point in time during the month of December. Sketch a picture and show all your work.

Answer 1

Step-by-step explanation:

Santa's initial weight = 185 pounds

He will need to gain 4 and a quarter pounds of weight each day.

• Let the number of days = x

,

• His weight =y

A linear function to represent his weight at any point in time during the month of December will be:

`y=4(1)/(4)x+185`

Weight on December 24th

The number of days, x=24

Therefore:

`\begin{gathered} y=4(1)/(4)x+185 \\ =(17)/(4)*24+185 \\ =102+185 \\ y=287\text{ pounds} \end{gathered}`

Santa’s weight on December 24th will be 287 pounds.

Graph

We graph the linear function using the x and y-intercepts.

`\begin{gathered} \text{When x=0} \\ y=4(1)/(4)x+185 \\ y=4(1)/(4)(0)+185 \\ y=185 \\ \implies\text{The point (0,185)} \end{gathered}`

Similarly:

`\begin{gathered} \text{When x=0} \\ y=4(1)/(4)x+185 \\ y=4(1)/(4)(0)+185 \\ y=185 \\ \implies\text{The point (0,185)} \end{gathered}`

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