Question

Each suitcase is 14 1/6 inches tall. Your plan is to stack all four suitcases on top of one another in your trunk. If your trunk is only 50 inches high, will you have enough room?

Answer 1

Each suitcase is 14 1/6 inches tall. Your plan is to stack all four suitcases on top of one another in your trunk. If your trunk is only 50 inches high, will you have enough room?

No, the height of all the suitcases is 52 2/3
inches.

No, the height of all the suitcases is 56 2/3
inches.

Yes, the height of all the suitcases is 48 and 2/3 inches.

No, the height of all the suitcases is 56 5/6
inches.

Answer 2

To determine if you have enough room in your trunk to stack all four suitcases, you'll first need to calculate the total height of the four suitcases.

Each suitcase is 14 1/6 inches tall. To find the total height of four suitcases, you can multiply the height of one suitcase by four:

\[
\text{Total height} = 4 \times 14 \frac{1}{6}
\]

First, convert \( 14 \frac{1}{6} \) to an improper fraction:

\[
14 \frac{1}{6} = \frac{14 \times 6 + 1}{6} = \frac{84 + 1}{6} = \frac{85}{6}
\]

Now, multiply this by 4:

\[
\text{Total height} = 4 \times \frac{85}{6} = \frac{340}{6}
\]

Next, simplify \( \frac{340}{6} \):

\[
\frac{340}{6} = \frac{170}{3} \approx 56.67 \text{ inches}
\]

Now, compare this total height to the height of the trunk:

- Trunk height: 50 inches
- Total height of the suitcases: approximately \( 56.67 \) inches

Since \( 56.67 \) inches is greater than 50 inches, you will **not** have enough room to stack all four suitcases in your trunk.

Answer 3

Let's calculate the total height of the four suitcases again to confirm the correct value.

Each suitcase is \( 14 \frac{1}{6} \) inches tall. To convert \( 14 \frac{1}{6} \) to an improper fraction:

\[
14 \frac{1}{6} = \frac{14 \times 6 + 1}{6} = \frac{84 + 1}{6} = \frac{85}{6} \text{ inches}
\]

Now, calculate the total height of four suitcases:

\[
\text{Total height} = 4 \times \frac{85}{6} = \frac{340}{6} = \frac{170}{3} \text{ inches}
\]

Now, let's convert \( \frac{170}{3} \) to a mixed number:

1. Divide 170 by 3, which gives 56 with a remainder of 2.
2. Therefore, \( \frac{170}{3} = 56 \frac{2}{3} \) inches.

Now we can compare this with the height of the trunk, which is 50 inches.

Since \( 56 \frac{2}{3} \) inches is greater than 50 inches, you **will not** have enough room.

So the correct answer is: **No, the height of all the suitcases is 56 2/3 inches.**