SOLUTION: the sales price of a car is $12,590, which is 20% off the original price. What is the original price? I tried multiplying 20% of the sales price and adding it back on but si

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: the sales price of a car is $12,590, which is 20% off the original price. What is the original price? I tried multiplying 20% of the sales price and adding it back on but si      Log On


   

Question 448085: the sales price of a car is $12,590, which is 20% off the original price. What is the original price?
I tried multiplying 20% of the sales price and adding it back on but since the price given is already 20% off it would not be correct. So I need to find 20% of what amount is $12,590 but not sure what formula to use!
Also, If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together? I know it will be less that 4 and more than 2 but not sure of what formula to use!
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.


Let x = original price of the car (ie the price before the discount is applied. So this means that the original price is more than the sale price).


Since the sale price is 20% off of the original price, this means that we have the following

Sale price = Original Price - 20% of original price

In other words, we're subtracting 20% of the original price from the original price.


In our problem, we let x be the original price. Now 20% of the original price x is 0.2x (note: 20% in decimal form is 0.2, just move the decimal point 2 spots to the left)


So we now get

Sale Price = x - 0.2x


But we also know that the sale price was $12,590. So this means that


12590 = x - 0.2x


Now combine like terms on the right side to get


12590 = 0.8x


Note: x - 0.2x = 1x-0.2x = (1-0.2)x = 0.8x


Now we want to isolate x. We do this by noticing that 0.8x means "0.8 times x". So to undo multiplication, we use division. This means we divide both sides by 0.8


Divide both sides by 0.8 to isolate x and get


12590/0.8 = x


15737.5 = x <----- Use a calculator to get this


x = 15737.5


So because x = 15737.5 and x is the original price, this means that the original price was $15,737.50


Notice how the original price ($15,737.50) is more than the sale price ($12,590). Also, notice that if you take 20% off of the original price ($15,737.50), you get the sale price ($12,590). Let's check that

Check:

20% of $15,737.50 is 0.2*15737.50 = 3147.5


Subtract this from the original price to get


15737.50 - 3147.5 = 12590


So this verifies the answer.