Salary plus Commision Equation

Question

Jasmin gets paid a base salary of $700 a week. She also gets paid an additional $20 for ever 50 items she sells.

I have to write an expression to represent this relationship. I have an equation but I don't know how to make it work for $20 for every 50 items instead of adding a percent of $20 for every item.

P = Pay check N = Number of Items Sold

P = $700 + (N/50) x $20

It works fine if the number of items sold is a multiple of 50 but fails if it any other number

Example:

P = $700 + (50/50) x $20 = $720 It Works!

P = $700 + (82/50) x $20 = $732.8 It fails it should be $720 because she only sold 1 group of 20 items so she should only get an extra $20 not a percent of $20.

How do I fix my equation So it works all the time?

Answer 1

What you are describing is the "floor" function:

P = 700 + ⌊(N/50)⌋ * 20

where ⌊x⌋ ≡ floor(x) = { the greatest integer less than or equal to x }