High School

Joseph wants to convert 145 pounds to kilograms. He knows his conversion factor is: [tex]1 \, \text{lb} = 0.45 \, \text{kg}[/tex].

Which train track shows the correct way to set up the problem?

A.
[tex]
\[
\begin{array}{c|c}
145 \, \text{lb} & \, \text{kg} \\
\hline
1 &
\end{array}
\]
[/tex]

B.
[tex]
\[
\begin{array}{c|l}
145 & \\
\hline
1 &
\end{array}
\]
[/tex]

C.
[tex]
\[
\begin{array}{c|c}
145 \, \text{kg} & \, \text{lb} \\
\hline
1 &
\end{array}
\]
[/tex]

Answer :

To convert 145 pounds to kilograms using the given conversion factor [tex]\(1 \text{ lb} = 0.45 \text{ kg}\)[/tex], follow these steps:

1. Identify the conversion factor: We are provided with the conversion factor that states [tex]\(1 \text{ lb} = 0.45 \text{ kg}\)[/tex]. This means that for every pound, there are 0.45 kilograms.

2. Set up the conversion: You want to convert 145 pounds into kilograms. To do this, you multiply the number of pounds by the conversion factor:
[tex]\[
\text{Kilograms} = \text{Pounds} \times \text{Conversion Factor}
\][/tex]

3. Substitute the values: Plug in 145 for the pounds and 0.45 for the conversion factor:
[tex]\[
\text{Kilograms} = 145 \times 0.45
\][/tex]

4. Calculate the result: Perform the multiplication to find the equivalent weight in kilograms:
[tex]\[
\text{Kilograms} = 65.25
\][/tex]

Therefore, 145 pounds is equal to 65.25 kilograms.

Now, regarding the train track method you asked about, the correct setup for this conversion would be:

[tex]\[
\begin{tabular}{c|c}
145 \text{ lb} & \text{kg} \\
\hline
1 &
\end{tabular}
\][/tex]

This setup shows that you start with 145 pounds and use the conversion factor [tex]\(0.45 \text{ kg per lb}\)[/tex] to convert to kilograms, following the same logic we used in the calculations.