Question

(b) the other container has a volume of 22\frac{1}{2} ft^{3}, a length of 5 ft, and a height of 1\frac{1}{2} ft. find its width.

Explanation:

Step1: Convert mixed numbers to improper fractions

The volume \(V = 22\frac{1}{2}=\frac{22\times2 + 1}{2}=\frac{45}{2}\) \(ft^{3}\), the height \(h=1\frac{1}{2}=\frac{1\times2+1}{2}=\frac{3}{2}\) \(ft\), and the length \(l = 5\) \(ft\).
The formula for the volume of a rectangular prism is \(V=l\times w\times h\).

Step2: Solve for the width \(w\)

We can rewrite the formula for \(w\) as \(w=\frac{V}{l\times h}\).
Substitute the values: \(l\times h=5\times\frac{3}{2}=\frac{15}{2}\).
Then \(w=\frac{\frac{45}{2}}{\frac{15}{2}}\).
When dividing by a fraction, we multiply by its reciprocal: \(w=\frac{45}{2}\times\frac{2}{15}\).
Cancel out the common factors: \(\frac{45}{2}\times\frac{2}{15}=\frac{45\times2}{2\times15}=\frac{45}{15}=3\).

Answer:

\(3\)