Question

A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the nearest nickel?

Answer 1

Ok, so the discount is given in a percentage, in this case 10%. The sale price is going to reflect 10% of the original price minus the discount, so...

Sale $ = original$ - original $ x .10

If we use some algebra, we can reorganize the equation to solve for the original price...

Sale $ = original$ - original $ x .10
Sale $ = original$ (1 - .10)
Sale $ = original$ x .90
original$ = sale$/.90

So now we can plug in our values

original price = 50/.90
original price = 55.55555 = $55.55 to the nearest nickel

Answer 2

$55.55

Explanation:

In order to calculate the original price of the radio we just have to do a rule of thirds, we know that the price payed was $50, and that it was 10% off from the original price, now we just have to to a simple rule of thirds, if $50 is the 90% how much is the 100%?

`(50)/(x) =(90)/(100)`

Now we clear X to find how much is the 100%:

`x=(50x100)/(90) \\x=(5000)/(90) \\x=55.5555`

So the original price was $55.55