Problem Solving

A certain candy manufacturer reduced the weight of Candy Bar M by 20 percent but left the price
unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?

a)5%
b)10%
c)15%
d)20%
e)25%

We are given that a certain candy manufacturer reduced the weight of Candy Bar M by 20 percent but left the price unchanged. If we let w = the original weight of the bar, the new weight is 0.8w = 4w/5. If we let p = the original price of the bar we know:

p/w = the original price per ounce of the bar

p/(4w/5) = 5p/4w = the new price per ounce of the bar

Finally we can determine the resulting percent increase in the price per bar due to the change:

[5p/4w - p/w]/[p/w] x 100

[5p/4w - 4p/4w]/[p/w] x 100

[p/4w]/[p/w] x 100

p/4w x w/p x 100 = 1/4 x 100 = 25%

Answer: E

Alternate Solution:

Rather than use letters, we can use convenient numbers to answer the question.

Let's let the original price of the candy be $20, with a weight of 10 ounces. Thus, the original price per ounce is 20/10 = $2.00 per ounce.

The new bar has the same price of $20, but the weight has been reduced by 20%, making the new weight 10 x 0.8 = 8 ounces. Now, the new price per ounce is 20/8 = $2.50 per ounce.

We use the percent change formula, which is (New price - Old price)/Old price x 100%. We obtain:

(2.50 - 2.00)/2.00 x 100%

.5/2 x 100% = 5/20 x 100% = 25%