|
Question 1089956: I have a car I take 10% off them another 15% of the sold price is 11475 what is the original price
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if i understand you correctly, your first discount is 10% off the retail price and then your second discount is another 15% off the first discount price.
your final selling price is 11475.
we'll do this logically first and then we'll do it using algebraic notation.
you start with the retail price.
you take 10% off the retail price.
your discount price is equal to the retail price minus 10% of the retail price which makes your discount price equal to 90% of the retail price.
next you start with the discount price.
you take 15% off the discount price.
your final price is equal to the discount price minus 15% of the discount price which makes your final price equal to 85% of the discount price.
your final price is 85% of your discount price which is 90% of your retail price.
that makes your final price equal to 85% of 90% of your retail price.
that would make it equal to .85 * .90 times your retail price.
that would make it equal to .765 times your retail price.
your final price is equal to .765 times your retail price.
your final price is 11475.
that makes your retail price equal to 11475 / .765 = 15000.
to confirm, your retail price is 15000 and you take off 10%.
that makes your discount price equal to 13500.
you take another 15% off 13500 to get a final selling price of 11475.
everything checks out so the solution is good.
now we'll solve it algebraically.
you pretty much do the same thing except except you assign variables to represent the values of what you're working with, and you use algebraic rules to simplify and solve.
let x be equal to the retail price.
let y be equal to the discount price.
let z be equal to the final price.
the discount price is 10% off the retail price.
therefore y = x - .10 * x
the final price is 15% off the discount price.
therefore z = y - .15 * y
you know that the final price is 11475.
therefore z = 11475.
z = y - .15 * y becomes 11475 = y - .15 * y
factor out the y and you get 11475 = y * (1 - .15)
simplify and you get 11475 = y * .85
divide both sides of this equation by .85 and you get 11475 / .85 = y
solve for y and you get y = 11475 / .85 = 13500
now that you know the value of y, you go back to the equation of y = x - .10 * x
replace y with 13500 and you get 13500 = x - .10 * x
factor out the x and you get 13500 = x * (1 - .10)
simplify to get 13500 = x * .90
divide both sides of the equation by .9 and you get 13500 / .90 = x
solve for x to get x = 13500 / .90 = 15000
x is the retail price which is equal to 15000
y is the discount price which is equal to 13500.
z is the final price which is equal to 11475.
to simplify the chain of events.
y = .90 * x
z = .85 * y
since y = .90 * x, replace y with .90 * x to get z = .85 * (.90 * x)
using rules of multiplication, this is equivalent to (.85 * .90) * x which is equal to .765 * x
so you get z = .765 * x
z is the final price.
you get 11475 = .765 * x
solve for x to get x = 11475 / .765 = 15000
x represents the retail price, therefore the retail price is equal to 15000.
the retail price is equal to the original price, therefore the original price is equal to 15000.
|
|
|
| |
