Problem Solving

yvonne12 wrote: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 the candy bar M?

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%

Alternate Solution:

Let's assume the candy bar's original weight was 20 ounces, and its cost was $1.60. Thus, its original cost per ounce was $0.08, or 8 cents.

The new candy bar weighs 20 x 0.8 = 16 ounces, and its cost is unchanged, so it is still $1.60. Thus, the cost per ounce of the new candy bar is $0.10, or 10 cents.

We calculate the percent increase, using the formula: (New - Old)/Old x 100 to obtain:

(10 - 8)/8 x 100 = 0.25 x 100 = 25%.