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

Responses

c−58=39 and 97

c−58=39 and 97

c+39=58 and 19

c+39=58 and −19

9 answers

To determine how many cans are already on the shelf, let's define \( c \) as the number of cans already on the shelf.

According to the problem, the shelf can hold a total of 58 cans, and Alexei can still put 39 more cans on it. This gives us the equation:

\[ c + 39 = 58 \]

Now, let's solve for \( c \):

  1. Subtract 39 from both sides of the equation: \[ c = 58 - 39 \]
  2. Calculate the right-hand side: \[ c = 19 \]

This means there are currently 19 cans on the shelf.

So the correct equation and answer from the choices provided are:

\( c + 39 = 58 \) and \( 19 \).

Trey is running in a race. He has completed 14 of the race so far. He has already run 1.2 miles. How many more miles must Trey run to complete the race
Responses:

5.2 miles

1.6 miles

0.3 miles

3.6 miles

To find out how many more miles Trey must run to complete the race, we need to have information about the total distance of the race. However, from the information given, it appears there is some confusion about what "14 of the race" means — it might be interpreted as 14% or some other fraction of the total distance.

Assuming "14 of the race" refers to Trey completing 14 segments (or parts) of a unit that equals the total distance of the race, we can proceed as follows:

  1. Determine the total distance of the race.
  2. Subtract the distance he has already run (1.2 miles) from this total distance to find out how many more miles he needs to run.

Let's assume the total distance of the race is represented as \( T \). If Trey has already run 1.2 miles, the equation will look like this:

\[ \text{Miles remaining} = T - 1.2 \]

Since we don't have the total distance \( T \), we can conceptualize it with the given options:

Let's make an estimation from the provided choices on the total distance:

If we consider \( T \) as \( 5.2 + 1.2 \) miles = 6.4 miles, Trey's remaining distance would be:

\[ 6.4 - 1.2 = 5.2 \text{ miles} \]

If we consider \( T \) as \( 1.6 + 1.2 \) miles = 2.8 miles, the remaining distance would be:

\[ 2.8 - 1.2 = 1.6 \text{ miles} \]

If we consider \( T \) as \( 0.3 + 1.2 \) miles = 1.5 miles, the remaining distance would be:

\[ 1.5 - 1.2 = 0.3 \text{ miles} \]

If we consider \( T \) as \( 3.6 + 1.2 \) miles = 4.8 miles, the remaining distance would be:

\[ 4.8 - 1.2 = 3.6 \text{ miles} \]

Since we have too many unknowns, we can only conclude based on the scenarios. If we are looking for a reasonable total distance or remaining distances, it would be likely based on some common race distances.

Assuming a standard race distance (which can be 3.1 miles for a 5K or similar), the question could imply:

For a race distance of 6.4 miles:

  • If he ran 1.2 miles, then he has to run 5.2 miles more.

If the race is meant for shorter events or half events, we can derive the proportionality.

Conclusion: Without specific total distance in context, provided the options, the most reasonable assumption for a total race completion would mean that the correct response to how many more miles Trey must run is:

5.2 miles.

Carlos is playing basketball this season. He is trying to average 25 points per game. He has scored 27, 18, 24, 32, 15, and 27 points in the previous 6 games. What equation can help you find the score for the last game that will give Carlos an average of 25 points
Responses

27+18+24+32+15+27/7+s=25

27+18+24+32+15+1/7+s7=25

27+18+24+32+15+2/7+s7=25

143s/7=25

To find the score Carlos needs to achieve in his last game to average 25 points over 7 games, we can start by defining the terms.

  1. Total points needed for 7 games to average 25 points: \[ 25 \text{ points/game} \times 7 \text{ games} = 175 \text{ points} \]

  2. Points scored in the first 6 games: We sum the points scored in the six games: \[ 27 + 18 + 24 + 32 + 15 + 27 = 143 \]

  3. Equation to find the score needed in the last game: Let \( s \) be the score Carlos needs in the last game. The equation to represent his total score for 7 games is: \[ 143 + s = 175 \]

Now, we can express this equation in a different way, isolating \( s \): \[ s = 175 - 143 \] \[ s = 32 \]

Evaluating the Given Response Options:

None of the provided responses expresses this equation directly. However, we can analyze them:

  1. Option 1: \((27+18+24+32+15+27)/7 + s = 25\)

    • This suggests averaging the first 6 scores and adding \( s \) to get 25. However, this would not equal 25, because it averages over 7 scores.
  2. Option 2: \((27+18+24+32+15+1)/7 + s/(7) = 25\)

    • The addition of "1" is incorrect and does not represent the initial scores accurately.
  3. Option 3: \((27+18+24+32+15+2)/7 + s/(7) = 25\)

    • Again, there is incorrect data with the addition of "2".
  4. Option 4: \(\frac{143+s}{7}=25\)

    • This one correctly represents the situation because it states that the sum of the current total and the required score divided by the number of games played (7) equals the target average (25).

Conclusion:

The correct equation that will help find the score for the last game that will give Carlos an average of 25 points is:

\(\frac{143 + s}{7} = 25\).

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
Responses:

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

To solve this problem, we need to establish an inequality that represents the club's sales situation.

  1. Define the variables: Let \( b \) be the number of candy bars sold. The club sells each candy bar for $2.

  2. Calculate the revenue from selling \( b \) candy bars: The revenue from selling \( b \) bars is given by: \[ 2b \]

  3. Determine the costs: The club bought the bars for $400, so this is their fixed cost.

  4. Set the inequality for profit: The club needs to make at least $1,000 to go on their trip. Thus, the profit (revenue minus costs) needs to be at least $1,000: \[ \text{Profit} = \text{Revenue} - \text{Cost} \geq 1000 \] Substituting the expressions for revenue and costs, we have: \[ 2b - 400 \geq 1000 \]

This is the inequality that represents the club's situation.

  1. Solving the inequality: Let's solve this inequality to see how many candy bars need to be sold to make at least $1,000: \[ 2b - 400 \geq 1000 \] Add 400 to both sides: \[ 2b \geq 1400 \] Divide both sides by 2: \[ b \geq 700 \]

Conclusion:

The club needs to sell at least 700 candy bars to make enough profit.

Now, considering the total of 725 bars they have:

  • Since \( 725 \geq 700 \), they can sell enough bars to meet their goal.

Final Answer:

The inequality that best represents this problem is: \( 2b - 400 \geq 1000 \), 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)
Responses

h−5=42 and h=47, which is not viable.

5h=42, so h=8.4 horses, which is viable.

h5=42 and h=210, which is not viable.

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

To find out how many horses the trainer can train based on the number of treats she has, we'll define \( h \) as the number of horses. The trainer uses 5 treats per horse for a training session.

Establishing the Equation:

The total number of treats she has is 42 mints. Thus, the equation that relates the number of horses \( h \) to the total number of mints is:

\[ 5h = 42 \]

This equation means that 5 mints (treats) are needed for each horse and the total number of mints is 42.

Solving the Equation:

Now let's solve the equation for \( h \):

\[ h = \frac{42}{5} = 8.4 \]

This means that theoretically, she could train 8.4 horses.

Viability of the Solution:

Since you cannot train a fractional horse, training 8.4 horses is not practically viable. Therefore:

  • The maximum number of whole horses she can train is 8 horses (since she can only use whole mints per horse).

Reviewing the Responses:

  1. \( h - 5 = 42 \) and \( h = 47 \), which is not viable.

    • This does not correctly represent the situation.
  2. \( 5h = 42 \), so \( h = 8.4 \) horses, which is viable.

    • The equation is correct, but the statement about it being viable is not true.
  3. \( h5 = 42 \) and \( h = 210 \), which is not viable.

    • This does not correctly represent the situation.
  4. \( 5h = 42 \), so \( h = 8.4 \) horses, which is not viable.

    • This is correct because the equation is accurate, and \( h = 8.4 \) is not a viable option.

Conclusion:

The most accurate response based on the context of the problem is:

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