Wiyot is earning money for a longboard by selling lemonade at the soccer fields

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 N.,

We can set day one equal to, a₁ = 33.

And using a arithmetic explicit formula a_n = a₁ + (n - 1)*d, with d = 6.

For day eight (a₈) with n = 8:

a₈ = 33 + (8 - 1)*6 = 33 + 42 = 75

The sum for an arithmetic series is: S_n = [n*(a₁ + a_n)]/2

With n = 8:

S₈ = [8*(33 + 75)]/2 = 432

Therefore at day eight, 432 cups have been sold.

(You can check by adding 33+39+45+51+57+63+69+75=432).

I hope this helps, Joe.