the price of a soda went down by 20%...

Question

The price of a soda went down by 20%. The new, reduced price is $400. 

a) Explain why you can use the next percent diagram to calculate the price of the sofa before the education. (Fill in steps as needed.)

   80% -> $400

   100% -> ___

Where does the 80% come from, and why is it equated with $400?

b) Explain why you CAN'T calculate the price of the sofa before the reduction by increasing $400 by 20%. 

Answer 1

(A)

 

If the price went down by 20%, then the final price must be 100% - 20% = 80% of the original price.  That means the final price of $400 is 80% of the original price.

 

Set up a proportion:

 

80% is to $400 as 100% is to x, where x = original price.

 

80% → $400

100% → x

 

x = (100%)*($400) / (80%) = $500

 

The original price is $500.

 

(B)

 

Increasing the $400 by 20% does not work because you are adding 20% to a smaller number, as opposed to subtracting 20% from a larger number.  In this problem, if you subtract 20% from $500, you get $400.  But if you add 20% to $400, you get $480.  That is because the 20% reduction of the larger number ($500) is not the same as the 20% increase of the smaller number ($400).

 

However, you can still get the original price from the reduced price by dividing by the percentage that the reduced price is of the original price.  You need to use the decimal form of the percentage.

 

80% is 0.80 of the original.

 

x = $400 / 0.80 = $500