Maths problem

Question

The price of a shirt is increased by 10% for GST and then decreased by 10% for a sale. The new price is $44 , what was the original price.

Answer 1

The new price of $44 is the result of a 10% tax applied and then a 10% sale applied. We'll work backwards to first find out the price after the tax but before the sale. If a 10% sale has been applied, then $44 is 90% of whatever the price was before.

 

So, we'd like to know what number (call it x) $44 is 90% of:

 

44 = 0.9x

48.89 = x

 

The price before the sale was $48.89.

 

Now we just need to undo the 10% sales tax. The original price (call it y) was increased by a 10% tax, meaning the price after the tax, $48.89, is 110% of y:

 

48.89 = 1.1y

44.44 = y

 

So, the original price of the shirt was $44.44.

 

 

 

To check our work, let's increase $44.44 by a 10% tax, then discount that by 10%:

 

(44.44(1.1))(0.9) = $44.00

 

That checks out!