Brandon wants to ride his bicycle 21 miles this week. He has already ridden 6 miles. If he rides for 5 more days, write and solve an equation which can be used to determine x*x*, the average number of miles he would have to ride each day to meet his goal.

To find the average number of miles \( x \) that Brandon needs to ride each day for the next 5 days to meet his goal, we can set up and solve an equation based on the total distance he wants to cover.

**Step 1: Define the variables and expressions.**

- Total miles Brandon wants to ride: 21 miles
- Miles already ridden: 6 miles
- Number of days left to ride: 5 days
- Average miles per day needed: \( x \)

**Step 2: Set up the equation.**

The total miles he needs to ride over the next 5 days, plus the 6 miles he has already ridden, must equal 21 miles:

\[
6 + 5x = 21
\]

**Step 3: Solve the equation for \( x \).**

1. Subtract 6 from both sides to isolate the term with \( x \):

\[
5x = 21 - 6
\]

2. Calculate the difference on the right-hand side:

\[
5x = 15
\]

3. Divide both sides by 5 to solve for \( x \):

\[
x = \frac{15}{5}
\]

4. Perform the division:

\[
x = 3
\]

So, Brandon needs to ride an average of **3 miles** each day for the next 5 days to meet his goal.

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Do you want details or have any questions?

Here are 5 related questions to consider:
1. What if Brandon only had 4 days left to ride? How would that change the average miles per day?
2. If Brandon rides 4 miles each day instead, how many total miles will he ride by the end of the week?
3. What if he had already ridden 8 miles instead of 6 miles? How would that affect the average miles per day?
4. If Brandon decides to ride an extra 2 miles on the first of the 5 days, how many miles per day would he need to ride on the remaining 4 days?
5. How would the equation change if Brandon's goal increased to 30 miles instead of 21 miles?

**Tip:** When distributing a total amount over several days, dividing by the number of days gives the average needed per day.

Learn how to solve the equation to find out how many miles Brandon needs to ride each day to meet his goal of 21 miles by the end of the week. This problem involves basic algebraic concepts, including linear equations and solving for an unknown variable. Suitable for students in Grades 6-8.

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