Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r . Then write a sentence to explain your answer.

Question

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Answer 1

Let's start the problem by determining how far Triana has left to travel after the first day. She has a total distance of 120 miles and she has already traveled 24 miles. Therefore, the remaining distance can be calculated as:

\[ 120 - 24 = 96 \text{ miles} \]

Triana wants to divide this remaining distance equally over the next three days. Let \( x \) represent the distance she will travel each day over the next three days. Since she will travel the same amount \( x \) for three days, we can express this as:

\[ 3x = 96 \]

Now, we can rewrite this equation in the form of \( px + q = r \):

\[ 3x + 0 = 96 \]

Next, we can solve for \( x \) by dividing both sides by 3:

\[ x = \frac{96}{3} = 32 \]

So, Triana will travel 32 miles each day for the remaining three days.

In conclusion, Triana will travel 32 miles each day for the next three days of her bike ride.

Answer 2

Ok but write what you explained to me with words

Answer 3

Triana is on a 120-mile bike ride and has already completed 24 miles on the first day. After this, she has 96 miles remaining to travel. She wants to distribute this remaining distance equally over the next three days. To find out how far she will travel each day, we can represent the daily distance as \( x \). The equation \( 3x = 96 \) shows that the total distance for the three days is equal to the remaining distance. Solving this, we find that \( x = 32 \). Therefore, Triana will travel 32 miles each day for the next three days of her ride.

Answer 4

Good job

Answer 5

Thank you! I'm glad you found the explanation helpful. If you have any more questions or need assistance with anything else, feel free to ask!

Answer 6

Ok I like your explanation but can you be more specific on the directions

Answer 7

Certainly! Here’s a revised explanation with more specific directions:

1. Identify Total Distance: Triana's bike ride has a total distance of 120 miles.

2. Calculate Distance Travelled on Day One: On the first day, she travels 24 miles.

3. Determine Remaining Distance: To find out how much distance she has left after the first day, subtract the distance traveled on the first day from the total distance: \[ 120 \text{ miles} - 24 \text{ miles} = 96 \text{ miles} \] So, she has 96 miles remaining.

4. Set Up the Equation: Let \( x \) represent the distance Triana will travel each day for the next three days. Since she will travel the same distance for those three days, we can express this relationship as: \[ 3x = 96 \] This means the total distance for the three days equals the remaining distance of 96 miles.

5. Rewrite the Equation: The equation can also be written in the form \( px + q = r \). In this case, it would be: \[ 3x + 0 = 96 \]

6. Solve for \( x \): To find the value of \( x \), divide both sides of the equation by 3: \[ x = \frac{96}{3} = 32 \]

7. Conclusion: Triana will travel 32 miles each day for the next three days of her bike ride.

Final Statement: Therefore, after the first day of traveling 24 miles, Triana will ride 32 miles each day for the three remaining days of her 120-mile bike ride.

Answer 8

Now explain it with words

Answer 9

Sure! Here’s the explanation using clear and specific wording:

Triana is on a bike ride that covers a total distance of 120 miles. On the first day of her bike ride, she travels 24 miles. After completing her first day, she still has some distance left to cover. To find out how much distance she has left, we subtract the distance she has already traveled from the total distance. This calculation shows that 120 miles minus 24 miles equals 96 miles. Therefore, Triana has 96 miles remaining to ride.

Next, Triana wants to divide this remaining distance equally over the next three days of her bike ride. To find out how far she will travel each day, we can use a variable to represent the daily distance. Let’s call the distance she travels each day \( x \). Since she will be riding for three days, we can express the total distance she will travel in those days as \( 3x \). This means that the total distance for her three remaining days should equal the 96 miles she has left.

To set up this relationship as an equation, we write \( 3x = 96 \). This equation indicates that the total distance for the three days, represented by \( 3x \), must equal the remaining distance of 96 miles.

We can simplify the equation by dividing both sides by 3. Doing this gives us \( x = 32 \). This means that Triana will travel 32 miles each day for the next three days.

In conclusion, Triana has already traveled 24 miles on the first day and now plans to ride 32 miles each day for the following three days to complete her 120-mile bike ride.

Answer 10

Ok now put it into 7 to 8 sentences

Answer 11

Triana is on a 120-mile bike ride and has completed 24 miles on the first day. After this, she has 96 miles remaining to travel. To evenly distribute this distance over the next three days, she lets \( x \) represent the distance she will bike each day. The equation \( 3x = 96 \) captures this relationship, indicating that the total distance for the three days equals the remaining distance. By dividing both sides of the equation by 3, we find that \( x = 32 \). This means Triana will travel 32 miles each day for the next three days of her trip. Thus, after biking 24 miles on the first day, she will cover 32 miles each day over the following days to complete her 120-mile ride.