Answer :
Certainly! Let's solve this step-by-step.
1. Understand the problem:
Joseph wants his average hiking pace over a weeklong trip to exceed 10 miles per day. We need to determine the inequality that represents the minimum number of miles, [tex]\( m \)[/tex], Joseph needs to travel over the week to exceed this pace.
2. Identify the given values:
- The average pace for a backpacker: [tex]\( 10 \)[/tex] miles per day.
- The duration of Joseph's trip: [tex]\( 7 \)[/tex] days.
3. Calculate the total miles needed for a specified average pace:
For Joseph to hike 10 miles per day over 7 days, he would need to cover:
[tex]\[ 10 \text{ miles/day} \times 7 \text{ days} = 70 \text{ miles} \][/tex]
This means if Joseph hikes exactly 70 miles in 7 days, his average pace will be 10 miles per day.
4. Determine the condition for exceeding the average pace:
Joseph wants to exceed an average pace of 10 miles per day. This means he needs to hike more than 70 miles in total over the 7 days.
5. Formulate the inequality:
If [tex]\( m \)[/tex] represents the total miles Joseph will travel, the inequality must ensure his total mileage is greater than 70 miles. This can be written as:
[tex]\[ m > 70 \][/tex]
Hence, the correct inequality that represents the number of miles [tex]\( m \)[/tex] that Joseph will travel on his trip is:
[tex]\[ \boxed{m > 70} \][/tex]
So, the correct answer is:
[tex]\[ (A) \, m > 70 \][/tex]
1. Understand the problem:
Joseph wants his average hiking pace over a weeklong trip to exceed 10 miles per day. We need to determine the inequality that represents the minimum number of miles, [tex]\( m \)[/tex], Joseph needs to travel over the week to exceed this pace.
2. Identify the given values:
- The average pace for a backpacker: [tex]\( 10 \)[/tex] miles per day.
- The duration of Joseph's trip: [tex]\( 7 \)[/tex] days.
3. Calculate the total miles needed for a specified average pace:
For Joseph to hike 10 miles per day over 7 days, he would need to cover:
[tex]\[ 10 \text{ miles/day} \times 7 \text{ days} = 70 \text{ miles} \][/tex]
This means if Joseph hikes exactly 70 miles in 7 days, his average pace will be 10 miles per day.
4. Determine the condition for exceeding the average pace:
Joseph wants to exceed an average pace of 10 miles per day. This means he needs to hike more than 70 miles in total over the 7 days.
5. Formulate the inequality:
If [tex]\( m \)[/tex] represents the total miles Joseph will travel, the inequality must ensure his total mileage is greater than 70 miles. This can be written as:
[tex]\[ m > 70 \][/tex]
Hence, the correct inequality that represents the number of miles [tex]\( m \)[/tex] that Joseph will travel on his trip is:
[tex]\[ \boxed{m > 70} \][/tex]
So, the correct answer is:
[tex]\[ (A) \, m > 70 \][/tex]
