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As a birthday gift, Lauren received a new monogrammed suitcase to take on the family trip to Ireland. The suitcase is shaped like a rectangular prism. It is $10$ inches deep and $20$ inches tall. The suitcase contains $2,600$ cubic inches of packing space. $\newline$ Which equation can you use to find the width of the suitcase, $w$ ? $\newline$ Choices: $\newline$ (A) $10 \times w \times 20 = 2,600$ $\newline$ (B) $10 \times 20 \times 2,600 = w$ $\newline$ What is the width of the suitcase? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ inches $\newline$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. As a birthday gift, Lauren received a new monogrammed suitcase to take on the family trip to Ireland. The suitcase is shaped like a rectangular prism. It is

10

inches deep and

20

inches tall. The suitcase contains

2,600

cubic inches of packing space.

\newline

Which equation can you use to find the width of the suitcase,

w

?

\newline

Choices:

\newline

(A)

10 \times w \times 20 = 2,600

\newline

(B)

10 \times 20 \times 2,600 = w

\newline

What is the width of the suitcase?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ inches

\newline

Identify Equation: Identify the correct equation to use for finding the width of the suitcase. Given the volume formula for a rectangular prism is $\text{length} \times \text{width} \times \text{height} = \text{volume}$ . Here, depth ( $10$ inches) and height ( $20$ inches) are given, and the volume is $2,600$ cubic inches. The equation to find the width ( $w$ ) is $10 \times w \times 20 = 2,600$ .
Solve Equation: Solve the equation $10 \times w \times 20 = 2,600$ for $w$ . First, simplify the left side: $10 \times 20 = 200$ . So, $200 \times w = 2,600$ .
Isolate Width: Divide both sides of the equation by $200$ to isolate $w$ . $2,600 / 200 = 13$ . So, $w = 13$ inches.

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