Alegbra word problem

Question

John collects old cans to turn in for money at a recycling company. He has collected 12,000 pounds of cans already, for which he could receive $4 per hundred pounds. He can continue collecting at 400 pounds per day. However the recycling comany has to lower its price by $0.10 per hundred pounds per day. How many days should he wait in order to get $490 for his his cans

Answer 1

The unit of measure is 100 pounds. So John presently has 120 units @ $4.00. He can collect 4 units more per day for "d" days. 

 

120 + 4d

 

The starting price for the cans is $4 per unit (one hundred pounds). Each day, "d," the price decreases $0.10.

 

4 - 0.1d

 

Money = pounds times price

 

490 = (120 + 4d)(4 - 0.1d)

490 = 480 + 16d - 12d - 0.4d²

10 = 4d - 0.4d²

0.4d² - 4d + 10 = 0

4d² - 40d + 100 = 0

d² - 10d + 25 = 0

(d - 5)(d - d) = 0

 

{5}

 

He should wait 5 days.