Question

Question 1 A)A large bin can store up to 44 towels. A small bin can hold three-fourths the volume of a large bin. You have already put 17 in the small bin. How many more towels can you store?(1 point) You can store up to $$ more towels. Question 2 A)You are playing a new video game. It says that you have completed 15 of the game. You have played for 23 minutes. Write and solve an equation to find how long it will take to complete your video game at this rate.(1 point) It will take $$ minutes to complete the game. Question 3 A)Oksana and her three friends are heading to a concert. They paid $540 in total for tickets. This included insurance for $15 for each person. How much was the cost of one ticket to the concert?(1 point) The cost for the one ticket to the concert was $$$. Question 4 A)Christiana makes $14 per hour working at the roller-skating rink. She needs to make $130 to pay her car insurance. How many hours should she work if she receives an $18 tip for hosting a birthday party that day?(1 point) She should work $$ hours to make $130. Question 5 A) A large dehumidifier removes 1.6 pints of water from the air around it per hour. The dehumidifier can hold up to 40 pints of water. Which option number represents the inequality that shows how much time the dehumidifier can run before it becomes full? Option #1: −1.6h≤40 Option #2: 1.6h≤40 Option #3: 1.6h≥40 Option #4: −1.6h≥40 (1 point) Option #$$ represents how long the dehumidifier can run before it becomes full.

Answer 1

Let's solve each of the questions in turn.

Question 1 A)
A large bin can hold 44 towels. A small bin holds three-fourths of a large bin. To find the capacity of the small bin: \[ \text{Capacity of small bin} = \frac{3}{4} \times 44 = 33 \text{ towels} \] You've already put 17 towels in the small bin, so the number of towels you can still store in the small bin is: \[ \text{Remaining capacity} = 33 - 17 = 16 \text{ towels} \] You can store up to 16 more towels.

Question 2 A)
You have completed 15% of the game by playing for 23 minutes. Let \( x \) be the total time to complete the game. The relationship can be set up as: \[ \frac{15}{100} = \frac{23}{x} \] Cross-multiply to solve for \( x \): \[ 15x = 23 \times 100 \] \[ 15x = 2300 \] \[ x = \frac{2300}{15} \approx 153.33 \text{ minutes} \] It will take approximately 153.33 minutes (or roughly 153 minutes) to complete the game.

Question 3 A)
Oksana and her three friends (4 people total) paid $540 for tickets, which included insurance of $15 for each person. The total cost for insurance is: \[ \text{Total insurance} = 4 \times 15 = 60 \] Subtract the insurance from the total cost to find the cost of the tickets: \[ \text{Cost of tickets} = 540 - 60 = 480 \] Now, to find the cost of one ticket: \[ \text{Cost per ticket} = \frac{480}{4} = 120 \] The cost for one ticket to the concert was $120.

Question 4 A)
Christiana makes $14 per hour and also receives an $18 tip. Let \( h \) be the hours she needs to work. The equation for her total earnings is: \[ 14h + 18 = 130 \] Subtract 18 from both sides: \[ 14h = 130 - 18 \] \[ 14h = 112 \] Now divide by 14: \[ h = \frac{112}{14} = 8 \] She should work 8 hours to make $130.

Question 5 A)
The dehumidifier removes 1.6 pints of water per hour and can hold up to 40 pints. The inequality representing how long it can run before it becomes full can be set as: \[ 1.6h \leq 40 \] So, Option #2: 1.6h ≤ 40 represents how long the dehumidifier can run before it becomes full.

Summary of Answers:

1. You can store up to 16 more towels.
2. It will take approximately 153.33 minutes to complete the game.
3. The cost for one ticket to the concert was $120.
4. She should work 8 hours to make $130.
5. Option #2 represents how long the dehumidifier can run before it becomes full.

Answer 2

Q2 is wrong

Answer 3

Let’s re-evaluate Question 2 carefully to find the correct equation and solution.

Question 2 A

You have completed 15% of the game in 23 minutes. We need to write and solve an equation to determine the total time it will take to complete the game at this rate.

Let \( T \) represent the total time to complete the game in minutes. Since 15% of the game has been completed in 23 minutes, we can set up the following proportion:

\[ \frac{15}{100} = \frac{23}{T} \]

Cross-multiply to get:

\[ 15T = 23 \times 100 \]

Calculating \( 23 \times 100 \):

\[ 15T = 2300 \]

Now, solve for \( T \):

\[ T = \frac{2300}{15} \approx 153.33 \text{ minutes} \]

However, this was already calculated in my previous response. If we need to find how much time remains to complete the game, we should first determine what 100% would represent based on the 23 minutes for 15%.

Now, if \( 23 \) minutes is 15%, we can calculate how long it takes to do 1%.

\[ \text{Time for } 1% = \frac{23}{15} \approx 1.5333 \text{ minutes} \]

To find the total time for \( 100% \):

\[ T = 1.5333 \text{ (minutes per percent)} \times 100 \approx 153.33 \text{ minutes} \]

Now, since you've completed 15% of it, the remaining percentage is:

\[ 100% - 15% = 85% \]

Now we calculate the time needed to complete the remaining 85%.

\[ \text{Remaining time} = 85 \times 1.5333 \approx 130.33 \text{ minutes} \]

Thus, it will take approximately 130.33 minutes to complete the game from this point onward.

Summary of Corrected Answer for Question 2:

It will take approximately 130.33 minutes (or about 130 minutes) to complete the game from where you are now. Thank you for your patience on this correction!

Answer 4

Remember that 23 minutes is the amount of time you have played so far. Check answer

Answer 5

Thank you for your patience. Let's reassess Question 2 again and provide a more precise solution with the correct context.

Question 2 A

The problem states that you have completed 15% of the game in 23 minutes. We need to find out how much longer it will take to finish the entire game at that same rate.

Let \( T \) be the total time (in minutes) to complete the game.

Since 15% of the game has been completed in 23 minutes, we set up the following relationship:

\[ \frac{15}{100} = \frac{23}{T} \]

Cross-multiplying gives us:

\[ 15T = 23 \times 100 \]

This simplifies to:

\[ 15T = 2300 \]

Now, solving for \( T \):

\[ T = \frac{2300}{15} \approx 153.33 \text{ minutes} \]

This means the total time to complete the game is approximately 153.33 minutes.

Now, since you have already played for 23 minutes, we need to calculate how much longer it will take to finish the game:

\[ \text{Remaining time} = T - 23 = 153.33 - 23 \approx 130.33 \text{ minutes} \]

Summary of the Correct Answer for Question 2:

It will take approximately 130.33 minutes (or about 130 minutes) more to complete the game. Thank you for your attention to detail!