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) Responses c+39=58 and 19 c plus 39 equals 58 and 19 c+39=58 and −19 c plus 39 equals 58 and negative 19 c−58=39 and 97 c minus 58 equals 39 and 97 c−58=39 and 97

To solve the problem, we need to determine how many cans are currently on the shelf, given that the shelf can hold a total of 58 cans and that Alexei can still put 39 cans on the shelf before it is full.

Let's define a variable:
- Let \( c \) be the number of cans already on the shelf.

According to the problem, the equation can be set up as follows:

\[
c + 39 = 58
\]

This equation means that the number of cans already on the shelf (c) plus the 39 additional cans he can still add equals the full capacity of the shelf (58 cans).

Now, we can solve this equation for \( c \):

\[
c + 39 = 58
\]

Subtract 39 from both sides:

\[
c = 58 - 39
\]
\[
c = 19
\]

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

Thus, the correct equation and answer are:
\[
c + 39 = 58 \quad \text{and} \quad c = 19
\]

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) Responses 0.3 miles 0.3 miles 5.2 miles 5.2 miles 3.6 miles 3.6 miles 1.6 miles

To determine how many more miles Trey must run to complete the race, we first need to figure out the total distance of the race.

We know that Trey has completed \( \frac{1}{4} \) of the race, which is equal to 1.2 miles. We can set up an equation to find the total distance \( d \) of the race:

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

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 need to find out how much more Trey must run to complete it. Since he has already run 1.2 miles, we can calculate the remaining distance:

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

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

The correct answer is **3.6 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?(1 point)

143s/7=25
27+18+24+32+15+27/7+s=25
27+18+24+32+15+27+s/7=25
27+18+24+32+15+17+s/7=25

To find the score Carlos needs in his last game to average 25 points per game after 7 games, we first need to calculate the total number of points he would need over the 7 games.

1. **Calculate the total points needed for 7 games:**
\[
\text{Average} = \frac{\text{Total Points}}{\text{Number of Games}}
\]
Rearranging gives:
\[
\text{Total Points} = \text{Average} \times \text{Number of Games}
\]
Therefore:
\[
\text{Total Points} = 25 \times 7 = 175 \text{ points}
\]

2. **Calculate the total points scored in the first 6 games:**
\[
27 + 18 + 24 + 32 + 15 + 27 = 143 \text{ points}
\]

3. **Set up the equation for the score \( s \) needed in the last game:**
We can express the total points as:
\[
143 + s = 175
\]

Now, to isolate \( s \):
\[
s = 175 - 143
\]
\[
s = 32
\]

However, from the choices given, we need to find the correct equation:

Among the options you provided, the equation that helps find the score for the last game that will give Carlos an average of 25 points is:

\[
\frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25
\]

This equation allows you to calculate the necessary score in the last game, so the correct choice is:

**27 + 18 + 24 + 32 + 15 + 27 + 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?(1 point) Responses 2b−400≥1000 , and no, it is not a viable option. 2 b minus 400 greater than or equal to 1000 , and no, it is not a viable option. 2b−400≥1000 , and yes, it is a viable option. 2 b minus 400 greater than or equal to 1000 , and yes, it is a viable option. 2b−400≤1000 , and no, it is not a viable option. 2 b minus 400 less than or equal to 1000 , and no, it is not a viable option. 2b−400≤1000 , and yes, it is a viable option.

To determine which inequality best represents the problem, let's break down the components of the situation:

1. **Revenue from selling candy bars:**
- Each candy bar sells for $2.
- If \( b \) represents the number of bars sold, then the revenue from selling \( b \) bars is \( 2b \).

2. **Cost of the candy bars:**
- The club bought 725 bars for $400, which is their total cost.

3. **Profit Calculation:**
- The profit can be expressed as:
\[
\text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400
\]

4. **Requirement for the trip:**
- The club needs to make at least $1,000 in profit to go on their trip. Therefore, we can set up the inequality:
\[
2b - 400 \geq 1000
\]

Now, let's simplify this inequality:
\[
2b - 400 \geq 1000
\]

To solve for \( b \):
1. Add 400 to both sides:
\[
2b \geq 1400
\]
2. Divide both sides by 2:
\[
b \geq 700
\]

**Conclusion About Viability:**
- The club has 725 bars, and since \( 725 \geq 700 \), they can indeed sell at least 700 bars to meet their requirement of making a profit of $1,000 or more.

### Summary:
The correct inequality that represents the problem is:
\[
2b - 400 \geq 1000
\]

And since 725 bars is enough to make the required profit, the answer is:
**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) Responses h−5=42 and h=47, which is not viable. h minus 5 equals 42 and h equals 47 , which is not viable. 5h=42, so h=8.4 horses, which is not viable. 5 h equals 42 , so h equals 8.4 horses, which is not viable. h5=42 and h=210, which is not viable. Start Fraction h over 5 End Fraction equals 42 and h equals 210 , which is not viable. 5h=42, so h=8.4 horses, which is viable.

To determine how many horses can be trained with the pink sugar mints, we need to set up an equation based on the problem's conditions.

### Given:
- Each training session requires 5 treats.
- The total number of mints available is 42.

### Equation Setup:
Let \( h \) represent the number of horses that can be trained. Since each horse requires 5 treats, the total number of treats used is \( 5h \).

To express the relationship mathematically, we set up the following equation:
\[
5h = 42
\]

### Solving for \( h \):
To find \( h \):
\[
h = \frac{42}{5} = 8.4
\]

This indicates that the trainer can train 8.4 horses. However, since you cannot train a fractional part of a horse, this means that only 8 whole horses can be trained with the available treats.

### Conclusion:
Now, let's evaluate the responses based on the calculations:
1. **Response:** \( 5h = 42, \) so \( h = 8.4 \) horses, which is **not viable.**

This response accurately reflects that the solution yields a non-integer value for the number of horses that can be trained, indicating it is not viable to train part of a horse.

Thus, the correct response is:
\[
5h = 42, \text{ so } h = 8.4 \text{ horses, which is not viable.}
\]

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=47, which is not viable.
5h=42, so h=8.4 horses, which is not viable.
h/5=42 and h=210, which is not viable.
5h=42, so h=8.4 horses, which is viable.

To determine how many horses the trainer can train with the available treats, let's analyze the situation again.

### Given:
- Each training session requires **5 treats per horse**.
- The trainer has **42 mints** total available.

### Equation Setup:
Let \( h \) represent the number of horses that can be trained. Since each horse requires 5 treats, we can set up the following equation:

\[
5h = 42
\]

### Solving for \( h \):
To find \( h \), divide both sides by 5:

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

Since you cannot train a fraction of a horse, this means that with 42 mints, she can train only **8 whole horses** before running out of treats.

### Analyzing the Responses:
1. **h−5=42 and h=47, which is not viable.**
- This equation is incorrect as it does not accurately represent the situation.

2. **5h=42, so h=8.4 horses, which is not viable.**
- This is correct; the equation accurately represents the scenario, but training 8.4 horses isn't possible as you can't have a fraction of a horse.

3. **h/5=42 and h=210, which is not viable.**
- This equation is incorrect, as it misrepresents the relationship between the number of horses and treats.

4. **5h=42, so h=8.4 horses, which is viable.**
- This is incorrect; while 5h=42 is accurate, stating it's viable when it gives a non-integer solution is wrong.

### Conclusion:
The best answer among the options provided is:
**5h = 42, so h = 8.4 horses, which is not viable.**

This response correctly indicates that while the equation is valid, the result is not a feasible option for the number of horses trained.