[email protected] wrote:To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 50%, and reduce the price it charges its consumers by 50% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?
No change
50%
100%
300%
400%
Old box:
Let e = 2 inches.
Volume = e³ = 2³ = 8 cubic inches.
Let the total price = $8.
Thus:
Price per cubic inch = (total price)/volume = 8/8 = $1.
New box:
Edge reduced by 50% = 50% of 2 inches = 1 inch.
New volume = 1³ = 1 cubic inch.
Price reduced by 50% = 50% of $8 = $4.
Thus:
New price per cubic inch = (new price)/(new volume) = 4/1 = $4.
Many students make SILLY MISTAKES when answering questions about percent change.
To make sure that we choose the correct answer choice, PLUG IN THE ANSWERS.
When the correct percentage is added to the old price per cubic inch -- $1 -- the resulting price must be $4.
Answer choice D: 300%
Adding 300% to $1, we get:
1 + (300/100)(1) = 1+3 = 4.
Success!
The correct answer is
D.
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