The total weight of the suitcase is 71 1/8

Question

The total weight of the suitcase is 71 1/8

After calculating the total weight, you and your friends have decided that you need to reduce the weight by 12.2 pounds (Ib.). Now, what is the total weight of the luggage? (2 points)
* 61.3 lb. 58.925 lb.
* 57.175 lb.
* 72.925 lb.

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? (2 points)
O No, the height of all the suitcases is 56 2/3 inches.
• No, the height of all the suitcases is 56 5/6 inches.
O Yes, the height of all the suitcases is 48 2/3 inches.
O No, the height of all the suitcases is 52 2/3 inches.

One of your suitcases has a rectangular bumper sticker that says, "California or bust!" plastered across the side. The length and width of the bumper sticker are 4.56 inches by 2.3 inches. What is the total area of the bumper sticker?
NOTE: A = 1 •w
(2 points)
O 10.488 in²
O 2.26 in²
• 20.7936 in²
O 6.86 in²

Answer 1

Bot GPT 4-o mini answered
2 hours ago

Let's solve each part step by step.

Part 1: Total Weight of the Luggage

The total weight of the suitcase is given as \(71 \frac{1}{8}\) pounds.

First, we need to convert \(71 \frac{1}{8}\) to an improper fraction:

\[ 71 \frac{1}{8} = \frac{71 \times 8 + 1}{8} = \frac{568 + 1}{8} = \frac{569}{8} \text{ pounds} \]

Next, we need to subtract 12.2 pounds from the total weight:

Convert \(12.2\) to a fraction:

\[ 12.2 = \frac{122}{10} = \frac{61}{5} \]

Now we need to subtract \(\frac{61}{5}\) from \(\frac{569}{8}\). To do this, we need a common denominator. The least common multiple of 8 and 5 is 40.

Convert both fractions:

\[ \frac{569}{8} = \frac{569 \times 5}{8 \times 5} = \frac{2845}{40} \] \[ \frac{61}{5} = \frac{61 \times 8}{5 \times 8} = \frac{488}{40} \]

Now, subtract the two fractions:

\[ \frac{2845}{40} - \frac{488}{40} = \frac{2845 - 488}{40} = \frac{2357}{40} \]

Now, divide to obtain a decimal:

\[ \frac{2357}{40} = 58.925 \text{ pounds} \]

So, the answer for this part is 58.925 lb.

Part 2: Height of the Suitcases

Each suitcase is \(14 \frac{1}{6}\) inches tall.

Convert \(14 \frac{1}{6}\) to an improper fraction:

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

If you stack 4 suitcases, the total height will be:

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

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

\[ \frac{170}{3} = 56 \frac{2}{3} \text{ inches} \]

Since the trunk is only 50 inches high and the height of all the suitcases is \(56 \frac{2}{3}\) inches, you will not have enough room.

So, the answer for this part is: No, the height of all the suitcases is 56 2/3 inches.

Part 3: Area of the Bumper Sticker

To find the area of the bumper sticker, use the area formula \(A = l \times w\):

\[ A = 4.56 \text{ in} \times 2.3 \text{ in} \]

Calculating this gives:

\[ A = 10.488 \text{ in}^2 \]

So, the answer for this part is 10.488 in².

Summary of Answers:

58.925 lb.
No, the height of all the suitcases is 56 2/3 inches.
10.488 in²