After the price of a CD player had been reduced by 1/4 of its original price, it was sold for $48. What was the original price?

Question

After the price of a CD player had been reduced by 1/4 of its original price, it was sold for $48.  What was the original price?

anonymous · Answer

original price is $64. 25 percent of 64 is 16 and 64-16=48

mathstudent55 · Answer

If the price was dropped by 1/4, that means it is now 3/4 of the original price.
The original price is the unknown, so call it x.
(3/4)x = 48
Solve for x by multiplying both sides by 4/3.

anonymous · Answer

why is it 3/4 x instead of 1/4 x??

mathstudent55 · Answer

The item cost originally x
Then the price was lowered by 1/4 of its original price, or (1/4)x discount
The new price is the original price, x, minus the discount of (1/4)x
So the new price is x - (1/4)x = (1/1)x - (1/4)x = (4/4)x - (1/4)x = (3/4)x
We are told that the new price is $48, and now we now the discounted price is (3/4)x, so we set them equal and solve the equation.

anonymous · Answer

ok that makes sense,, ty!!!

mathstudent55 · Answer

1/4 x is the discount amount. We were not told what dollar figure that is equal to.
So that does not help write the equation.
But 3/4 x as the discounted price is $48. That is enough info to write an equation.

mathstudent55 · Answer

wlcm