nhai2003 wrote:Computer Games Plus needs to get rid of its copies of an old computer game. If it lowers the cost of the old computer game by $5 dollars, it can increase sales of the old computer game by 10 units and still generate exactly $100 of revenue from the old game. How many units of the old computer game did Computer Games Plus sell after implementing the new selling strategy?
A) 10
B) 15
C) 20
D) 30
E) 50
please help me with this one. Thanks!
As noted, backsolving (working backwards from the choices) is a great approach on this type of question. In general, if the answer choices are numbers and you have a word problem with a simple question, backsolving is a great choice.
Of course, we could also solve algebraically:
x = original number of copies sold
p = original price
xp = (x + 10)(p - 5)
and
xp = 100
So:
100 = xp + 10p - 5x - 50
100 = 100 + 10p - 5x - 50
50 + 5x = 10p
10 + x = 2p
5 + x/2 = p
and subbing in:
x(x/2 + 5) = 100
(1/2)x^2 + 5x - 100 = 0
x^2 + 10x - 200 = 0
(x + 20)(x - 10) = 0
x = -20 or + 10
Negative solutions make no sense, so x=10.
Going back to the question: under the NEW plan, how many are sold:
so, we want (x + 10) = 20... choose (C).
After seeing the algebra, I'm sure you're on board with backsolving as a better approach!
