Please help me with this problem.
Paul wants to buy a stereo system. The store allows a 15% discount if the purchase is paid for within 30 days. 20% discount if the purchase is paid for within 10 days. If Paul pays $400 at the time of purchase. What was the original price? Thank you.

Question

Please help me with this problem.
Paul wants to buy a stereo system.  The store allows a 15% discount if the purchase is paid for within 30 days.  20% discount if the purchase is paid for within 10 days. If Paul pays $400 at the time of purchase. What was the original price?  Thank you.

espex · Answer

Well assuming the $400 pays the entire cost of the stereo, your total cost 'x' less 20% equals $400.
so x - .20x = 400, .8x = 400, 400/.8 = x, 500 = x

anonymous · Answer

Yes but using the same thinking and I use x-.15x =400, .85x=400, 400/.85=x, 470.59 would be the cost.  I think there is something wrong with this problem. Am I correct? Because there is two unknown the price and when he bought the stereo which was not given..

espex · Answer

Almost, the part you missed is that he paid $400 at the time of purchase, therefore, your equation would be x - .15x = 400 + y, there would need to be a second payment to have it paid off within the 11 - 30 day period. Perhaps there is another way of viewing this, let me study it for a minute.

espex · Answer

How about this, assuming that it is paid off in 30 days, the total price would be the 20% discount plus the 400 dollar payment plus 15% of the residual.$$x=.2x+400+.15(x-(400+.2x)) \rightarrow x=.2x+400+.15x-61-.3x$$$$x=.32x+339 \rightarrow .68x = 339 \rightarrow x=498.53$$ thus making the total price 498.53 and concluding that Paul made a residual payment of 98.53.

anonymous · Answer

OMG! Thank you so much for the help.  Now I can understand the problem. :) :)

espex · Answer

Glad to hear it. :)