A family-sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with dimensions 2 x 8 x 9 inches costs $4.50. What is the difference in price per cubic inch?

Marss
Nov 27, 2018

#1**+2 **

A box of cereal with dimensions 3in x 9in x 12in has a volume of 324in^3. The price of the box of cereal is $6. We can set up a proportion to determine the price per cubic inch:

\(\frac{\text{Price}}{\text{Cubic Inch}}=\frac{$6}{324in^3}=\frac{$1}{104in^3}\approx 0.00962\frac{\text{price}}{\text{in}^3}\)

A box of cereal with dimensions 2in x 8in x 9in has a volume of 104in^3. The price of the box is $4.50. Just like before, we can set up a proportion to determine the price per cubic inch:

\(\frac{\text{Price}}{\text{Cubic Inch}}=\frac{$4.50}{104\text{in}^3}=\frac{$9}{208\text{in}^3}\approx 0.04327\frac{\text{price}}{\text{in}^3}\)

Let's just find the difference of the simplified fractions of both boxes of cereal.

\(\frac{9}{208}-\frac{1}{104}\\ \frac{9}{208}-\frac{2}{208}\\ \frac{7}{208}\approx0.03365\frac{\text{price}}{\text{in}^3}\)

TheXSquaredFactor
Nov 27, 2018

#1**+2 **

Best Answer

A box of cereal with dimensions 3in x 9in x 12in has a volume of 324in^3. The price of the box of cereal is $6. We can set up a proportion to determine the price per cubic inch:

\(\frac{\text{Price}}{\text{Cubic Inch}}=\frac{$6}{324in^3}=\frac{$1}{104in^3}\approx 0.00962\frac{\text{price}}{\text{in}^3}\)

A box of cereal with dimensions 2in x 8in x 9in has a volume of 104in^3. The price of the box is $4.50. Just like before, we can set up a proportion to determine the price per cubic inch:

\(\frac{\text{Price}}{\text{Cubic Inch}}=\frac{$4.50}{104\text{in}^3}=\frac{$9}{208\text{in}^3}\approx 0.04327\frac{\text{price}}{\text{in}^3}\)

Let's just find the difference of the simplified fractions of both boxes of cereal.

\(\frac{9}{208}-\frac{1}{104}\\ \frac{9}{208}-\frac{2}{208}\\ \frac{7}{208}\approx0.03365\frac{\text{price}}{\text{in}^3}\)

TheXSquaredFactor
Nov 27, 2018