Question

One travel bag is 15 inches long, another is 18 inches long, and a third is 21 inches long. They are all 10 inches deep and 15 inches wide. Which travel bag can hold exactly 3,150 cubic inches? Explain your reasoning. 50 points to whoever answers

Answer 1

The travel bag that can hold exactly 3,150 cubic inches is the bag that is 21 inches long.

Explanation:

The travel bags can be modelled as rectangular prisms.

The formula for the volume of a rectangular prism is:

`\boxed{\textsf{Volume} = l * w* d}`

where:

• 
  `l` is the length.
• 
  `w` is the width.
• 
  `d` is the depth.

Given that all three bags have a depth of 10 inches and a width of 15 inches, we can create an equation for the volume of any of the bags by substituting d = 10 and w = 15 into the formula:

`\begin{aligned}\sf Volume &=l * w * d\\&= l * 15*10\\&=l * 150\\&=150\;l\end{aligned}`

To determine which travel bag can hold exactly 3,150 cubic inches, substitute volume = 3150 into the formula and solve for length, l:

`\begin{aligned}\sf Volume &=150\;l\\\\ \implies 3150&=150\;l\\\\(3150)/(150)&=(150\;l)/(150)\\\\21&=l\\\\l&=21\;\sf in\end{aligned}`

Therefore, the travel bag that can hold exactly 3,150 cubic inches is the bag that is 21 inches long.