A food company originally sells cereal in boxes with dimensions 25 cm by 14 cm by 10 cm. To make more profit, the company decreases each dimension of the box by x centimeters but keeps the price the same. If the new volume is 2,208 cm3 by how much was each dimension dec
Question
A food company originally sells cereal in boxes with dimensions 25 cm by 14 cm by 10 cm. To make more profit, the company decreases each dimension of the box by x centimeters but keeps the price the same. If the new volume is 2,208 cm3 by how much was each dimension dec
Solution
The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the original volume of the cereal box is V = 25 cm * 14 cm * 10 cm = 3500 cm^3.
The company then decreases each dimension by x cm, so the new dimensions are (25 - x) cm, (14 - x) cm, and (10 - x) cm.
The new volume is given as 2208 cm^3. So, we can set up the equation:
(25 - x) * (14 - x) * (10 - x) = 2208
This is a cubic equation in x, and solving it gives the value of x.
However, this is a complex cubic equation and may not be easy to solve by hand. You may need to use a calculator or a software tool that can solve cubic equations.
Once you solve for x, you will know by how much each dimension was decreased.
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