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Alexei is stocking a shelf at the store. The shelf can hold 58 cans, so he can still put 39 cans on the shelf before it is full. Create an equation to make sense of the problem and solve it to find out how many cans are already on the shelf. Which equation and answer are correct? (1 point)

c + 39 = 58 and 19
c - 58 = 39 and 97
c + 39 = 58 and -19
c - 58 = 39 and 97

21 answers

To understand the problem, we need to determine how many cans (let's denote this number as \( c \)) are already on the shelf. The shelf can hold a total of 58 cans, and since Alexei can still put 39 cans on the shelf, we can express this situation with the equation:

\[ c + 39 = 58 \]

This equation states that the number of cans already on the shelf (\( c \)) plus the number of cans that can still be added (39) equals the total capacity of the shelf (58).

Now we can solve for \( c \):

  1. Subtract 39 from both sides:

\[ c = 58 - 39 \]

  1. Calculate:

\[ c = 19 \]

Thus, the number of cans already on the shelf is 19.

The correct equation and answer from the options provided are:

c + 39 = 58 and 19.

Alexei is stocking a shelf at the store. The shelf can hold 58 cans, so he can still put 39 cans on the shelf before it is full. Create an equation to make sense of the problem and solve it to find out how many cans are already on the shelf. Which equation and answer are correct? (1 point)

c + 39 = 58 and 19
c - 58 = 39 and 97
c + 39 = 58 and -19
c - 58 = 39 and 97

To solve the problem, we need to establish an equation based on the information provided. We know:

  • The shelf can hold a total of 58 cans.
  • Alexei can still add 39 cans before the shelf is full.

Let \( c \) represent the number of cans already on the shelf. The equation that represents this situation is:

\[ c + 39 = 58 \]

Now, we'll solve for \( c \):

  1. Subtract 39 from both sides of the equation:

\[ c = 58 - 39 \]

  1. Calculate the right side:

\[ c = 19 \]

Therefore, the number of cans already on the shelf is 19.

The correct option from those provided is:

c + 39 = 58 and 19.

Trey is running in a race. He has completed 1/4 of the race so far. He has already run 1.2 miles. How many more miles must Trey run to complete the race? (1 point)
5.2 miles
3.6 miles
1.6 miles
0.3 miles

Let's first determine the total distance of the race. We know that Trey has completed \( \frac{1}{4} \) of the race and he has already run 1.2 miles.

To find the total distance of the race, we can set up the following equation:

\[ \frac{1}{4} \text{ of total distance} = 1.2 \text{ miles} \]

Let \( d \) represent the total distance of the race. Therefore, we can write:

\[ \frac{1}{4} d = 1.2 \]

To find \( d \), we can multiply both sides of the equation by 4:

\[ d = 1.2 \times 4 \] \[ d = 4.8 \text{ miles} \]

Now that we know the total distance of the race is 4.8 miles, we can find out how much more Trey needs to run to complete the race. Since he has completed 1.2 miles, we can calculate the remaining distance as follows:

\[ \text{Remaining distance} = d - \text{distance already run} \] \[ \text{Remaining distance} = 4.8 - 1.2 \] \[ \text{Remaining distance} = 3.6 \text{ miles} \]

Thus, Trey must run 3.6 miles more to complete the race.

The correct answer is 3.6 miles.

Trey is running in a race. He has completed 1/4 of the race so far. He has already run 1.2 miles. How many more miles must Trey run to complete the race? (1 point)

5.2 miles
3.6 miles
1.6 miles
0.3 miles

To find out how many more miles Trey must run to complete the race, let's first determine the total distance of the race.

We know:

  • Trey has completed \( \frac{1}{4} \) of the race.
  • He has run 1.2 miles during that time.

We can set up the equation:

\[ \frac{1}{4} \times \text{Total Distance} = 1.2 \text{ miles} \]

Let \( d \) represent the total distance of the race. So we have:

\[ \frac{1}{4} d = 1.2 \]

To find \( d \), we can multiply both sides by 4:

\[ d = 1.2 \times 4 \] \[ d = 4.8 \text{ miles} \]

Now that we know the total distance of the race is 4.8 miles, we can calculate how much farther he needs to run. Since he has already run 1.2 miles, we can find the remaining distance:

\[ \text{Remaining distance} = \text{Total Distance} - \text{Distance already run} \] \[ \text{Remaining distance} = 4.8 - 1.2 \] \[ \text{Remaining distance} = 3.6 \text{ miles} \]

Thus, Trey must run 3.6 miles more to complete the race.

The correct answer is 3.6 miles.

The adventure club is selling candy bars to go on their annual outing. The bars sell for $2 a bar. The club bought 725 bars for $400. The club needs to make at least $1,000 to go on their trip. Which inequality best represents this problem, and are the 725 bars a viable option to make enough profit? (1 point)
2b - 400 ≤ 1000 and no, it is not a viable option.
2b - 400 ≤ 1000, and yes, it is a viable option.
2b - 400 ≥ 1000 and no, it is not a viable option.
2b - 400 ≥ 1000 and yes, it is a viable option.

To determine the correct inequality and whether the selling of 725 candy bars is a viable option, let’s break down the information provided:

  1. Cost: The adventure club bought 725 bars for $400.
  2. Selling Price: Each bar is sold for $2.
  3. Minimum Required Revenue: The club needs to make at least $1,000 to go on their trip.

Step 1: Calculate Total Revenue from Selling Bars

Let \( b \) represent the number of bars sold. The revenue generated from selling \( b \) bars would be:

\[ \text{Revenue} = 2b \]

Step 2: Calculate Profit

The profit is calculated as:

\[ \text{Profit} = \text{Revenue} - \text{Cost} \] Using the values, we have:

\[ \text{Profit} = 2b - 400 \]

Step 3: Set Up the Inequality

The club needs the profit to be at least $1,000, so we can set up the inequality:

\[ 2b - 400 \geq 1000 \]

Step 4: Solve the Inequality

Now, let's solve the inequality for \( b \):

  1. Add 400 to both sides: \[ 2b \geq 1000 + 400 \] \[ 2b \geq 1400 \]

  2. Divide by 2: \[ b \geq 700 \]

Conclusion

This means they need to sell at least 700 bars to make at least $1,000 in profit.

Viability Check

The club has 725 bars available for sale. Since 725 is greater than the 700 bars required, this is indeed a viable option.

Final Answer

The correct inequality is:

2b - 400 ≥ 1000 and yes, it is a viable option.

The adventure club is selling candy bars to go on their annual outing. The bars sell for $2 a bar. The club bought 725 bars for $400. The club needs to make at least $1,000 to go on their trip. Which inequality best represents this problem, and are the 725 bars a viable option to make enough profit? (1 point)

2b - 400 ≤ 1000 and no, it is not a viable option.
2b - 400 ≤ 1000, and yes, it is a viable option.
2b - 400 ≥ 1000 and no, it is not a viable option.
2b - 400 ≥ 1000 and yes, it is a viable option.

To represent the situation mathematically, we need to establish the profit made from selling the candy bars and set up an appropriate inequality based on the requirements.

Given Information:

  • The selling price per candy bar: $2
  • Number of bars bought: 725
  • Cost of bars: $400
  • Minimum profit required: $1,000

Step 1: Calculate Total Revenue

If \( b \) is the number of bars sold, then the total revenue can be expressed as: \[ \text{Revenue} = 2b \]

Step 2: Calculate Profit

The profit is calculated as the revenue minus the cost: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

Step 3: Set Up the Inequality

Since the club needs to make at least $1,000, we can set up the following inequality: \[ 2b - 400 \geq 1000 \]

Step 4: Solve the Inequality

Now, we can solve this inequality to determine how many bars they need to sell:

  1. Add 400 to both sides: \[ 2b \geq 1000 + 400 \] \[ 2b \geq 1400 \]

  2. Divide both sides by 2: \[ b \geq 700 \]

Step 5: Check Viability with Available Bars

The club has 725 bars available for sale, which is greater than the minimum required (700 bars). Therefore, they can indeed sell enough bars to meet or exceed the required profit.

Conclusion

Based on the analysis, the correct inequality and viability conclusion are:

2b - 400 ≥ 1000 and yes, it is a viable option.

A horse trainer has a bag of pink sugar mints for horse treats. She needs five treats per training session. The bag holds 42 mints. Which equation shows the number of horses that she can train and is a solution a viable option? (1 point)
h/5 = 42 and h = 210, which is not viable.
5h = 42 so h = 8.4 horses, which is not viable.
5h = 42 so h = 8.4 horses, which is viable.
h - 5 = 42 and h = 47 which is not viable.

To determine the number of horses a trainer can train, we need to set up an equation based on the given information:

  1. Treats needed per training session: 5 treats
  2. Total treats in the bag: 42 mints

Step 1: Set Up the Equation

Let \( h \) represent the number of horses the trainer can train. If each horse requires 5 treats for the training session, the total number of treats used for \( h \) horses is \( 5h \).

Given that the total number of treats in the bag is 42, we can set up the following equation:

\[ 5h = 42 \]

Step 2: Solve the Equation

To find \( h \):

\[ h = \frac{42}{5} \]

Calculating this gives:

\[ h = 8.4 \]

Step 3: Determine Viability

Since \( h \) represents the number of horses, and it cannot be a fraction, training 8.4 horses is not practical. In real terms, the trainer can train at most 8 horses, as she cannot train a fraction of a horse.

Conclusion

Thus, the correct equation and analysis of the solution is:

5h = 42, so h = 8.4 horses, which is not viable.

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

To find out how many more towels can be stored, we first need to calculate the capacity of the small bin relative to the large bin.

Step 1: Determine the Capacity of the Small Bin

The capacity of the large bin is 44 towels. The small bin can hold three-fourths the volume of the large bin, so we can calculate the capacity of the small bin as follows:

\[ \text{Capacity of small bin} = \frac{3}{4} \times 44 = 33 \text{ towels} \]

Step 2: Calculate Remaining Capacity in the Small Bin

You have already put 17 towels in the small bin. To find out how many more towels can be added to the small bin, we subtract the number of towels currently in the small bin from its total capacity:

\[ \text{Remaining capacity} = \text{Capacity of small bin} - \text{Current towels} \]

Substituting the values:

\[ \text{Remaining capacity} = 33 - 17 = 16 \]

Conclusion

You can store up to 16 more towels in the small bin.

You are playing a new video game. It says that you have completed 1/5 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.

To determine how long it will take to complete the game, let's set up an equation based on the given information.

Step 1: Understand the Problem

You have completed \( \frac{1}{5} \) of the game in 23 minutes. We want to find out how long it will take to complete the entire game.

Step 2: Set Up the Equation

Let \( x \) be the total time (in minutes) it will take to complete the whole game. Since you have completed \( \frac{1}{5} \) of the game in 23 minutes, we can set up the following proportion:

\[ \frac{1}{5} \text{ of } x = 23 \]

Step 3: Solve for \( x \)

To isolate \( x \), multiply both sides of the equation by 5:

\[ x = 23 \times 5 \]

Calculating the right side gives:

\[ x = 115 \]

Conclusion

It will take 115 minutes to complete the game.

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 $?

To find the cost of one ticket to the concert, we can follow these steps:

Step 1: Calculate the Total Insurance Cost

There are 4 people (Oksana and her three friends), and each paid $15 for insurance. The total insurance cost can be calculated as follows:

\[ \text{Total Insurance Cost} = 4 \times 15 = 60 \]

Step 2: Calculate the Total Cost for Tickets

The total cost paid for tickets, which includes the insurance, was $540. To find the total cost spent on the tickets alone, we subtract the total insurance cost from the total amount paid:

\[ \text{Total Cost for Tickets} = 540 - 60 = 480 \]

Step 3: Calculate the Cost of One Ticket

The total cost for the tickets is $480, and since there are 4 people, the cost of one ticket can be determined by dividing the total ticket cost by the number of people:

\[ \text{Cost of One Ticket} = \frac{480}{4} = 120 \]

Conclusion

The cost for one ticket to the concert was $120.

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.

To determine how many hours Christiana should work to make $130 for her car insurance, we need to account for her hourly wage and the tip she receives.

Step 1: Determine the Total Amount Needed After Tips

Christiana needs to make $130 in total, and she will receive an $18 tip. Therefore, the amount she still needs to earn from working is:

\[ \text{Amount Needed from Work} = 130 - 18 = 112 \]

Step 2: Calculate Hours of Work Required

Christiana earns $14 per hour. To find out how many hours she needs to work to earn the remaining $112, we can set up the following equation:

\[ \text{Hours} = \frac{\text{Amount Needed from Work}}{\text{Hourly Wage}} = \frac{112}{14} \]

Calculating this gives:

\[ \text{Hours} = 8 \]

Conclusion

Christiana should work 8 hours to make $130 for her car insurance, considering her tip.