Wiyot is earning money for a longboard by selling lemonade at the soccer fields. Being a precocious and poorly-supervised 12 year old

Question

Wiyot is earning money for a longboard by selling lemonade at the soccer fields. Being a precocious and poorly-supervised 12 year old, Wiyot has no transportation and decides to use water from a nearby river.

Business is booming! He sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up. How many TOTAL cups of giardia-laced lemonade will Wiyot have sold by the time his parents get a call from county health officials on day 8?

Answer 1

Hi Svetlana! This questions models a linear system. In this case, Wiyot sold 33 lemonade cups on the first day and 6 cups for every day after that until the 8th day (ie. 6 on the second day, 6 on the third day and so forth). Using this, we would have the coordinates (1,33) , (2,39) and so on, where the x values represent the day and the y values represent the total amount of lemonade cups sold. Keep in mind that x must be greater than or equal to 1 and less than or equal to 8; we cannot have a day 0 or day 9 for example.

To find our equation, notice that 33 cups is the "starting point" followed by a constant rate (slope) of 6 cups sold each day thereafter. BUT we have to remember that 33 cups was sold when x = 1, or on day 1 and not on day 0. Furthermore, sales stops on day 8. So, our equation with the given conditions would be:

y = 33 + 6(x-1) where 1 <= x <= 8. (Where y is the total number of cups sold, and x is the day).

Another way we could have derived this equation is by writing in point-slope form using the coordinate (1,33) and slope = 6. Remember that point slope form is y - y1 = m(x - x1):

y - 33 = 6(x-1) which can be rewritten as y = 33 + 6(x-1) where 1<=x<= 8.

To find out how many total cups were sold, we simply plug in 8 into the equation:

y = 33 + 6(8-1) = 33 + 6(7) = 33 + 42 = 75 total cups. Hope this helps.