Word Problem help?

Question

Region C had sold 1500 boxes of cookies, region D sold 1200 boxes of cookies. If region D tries harder, they can sell 50 more boxes of cookies every day than region C. How many days will it take for Region D to catch up? Also, If sales are stopped after 8 more days, can you tell how many total boxes each region sold? Explain.

Answer 1

Let:

k = # of days
x = boxes of cookies sold by region C per a day

Therefore:
Region D is now selling x + 50 boxes of cookies per a day

The problem is asking for when Region D catches up to Region C.
Therefore we want:
Region C's current amount + amount of increase = Region D's current amount + amount of increase

with amount of increase = (# of days) * (boxes of cookies sold per day)
1500 + k * x = 1200 + k * (x + 50)
-1200              -1200
300 + k*x = k(x+50)
300 + kx = kx + 50k
       -kx     -kx
300 = 50k

Divide both sides by 50 and you get k = 6, so it will take 6 days Region D to catch up to Region C.

Also, you cannot tell how many total boxes each region sold after 8 days b/c you are not given any information on how many boxes of cookies are being sold per a day by Region C and/or D.