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# What is the difference in price per cubic inch?

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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?

#1
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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
+2294
+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