A company sells running shoes to dealers for $40 per pair if less than 50 pairs are ordered. If 50 or more pairs are ordered (up to 600), the price per pair is reduced at a rate of $0.04 times the number ordered. How many pairs can a dealer purchase for $8400?

To find the pattern, start plugging values in, and see what happens. First, note that ($40/pr)(50 pr) = $2000, so clearly the dealer will be working with the "50 or more" case.

pairs | price per | total |
50 | 40 - 0.04(50) | (40 - 0.04(50))(50) |
51 | 40 - 0.04(51) | (40 - 0.04(51))(51) |
52 | 40 - 0.04(52) | (40 - 0.04(52))(52) |
53 | | |
... | | |
x | | |

Once you see the pattern, you can create the "cost" formula in terms of "x" pairs of shoes. Set your formula equal to "8400", and solve for the value of x.

If you get stuck, please reply showing all of your steps and reasoning so far. Thank you!