Question

A student rode a bicycle fewer than 30 miles during a period of 5 days. The student rode 8 miles on Monday and m miles each day from Tuesday through Friday.



Which inequality represents all possible values of m

Answer 1

To determine the inequality that represents the total distance the student rode over the 5 days, we can start by adding the distance ridden on Monday to the distance ridden from Tuesday through Friday.

The distance ridden on Monday is 8 miles. The distance ridden from Tuesday to Friday (4 days) is represented as \( m \) miles per day. Therefore, the total distance ridden from Tuesday to Friday is:

\[
4m
\]

Now, we can express the total distance ridden over the 5 days as:

\[
8 + 4m
\]

According to the problem, the total distance is fewer than 30 miles. This gives us the inequality:

\[
8 + 4m < 30
\]

To solve the inequality for \( m \), we can first subtract 8 from both sides:

\[
4m < 30 - 8
\]
\[
4m < 22
\]

Next, we divide both sides by 4:

\[
m < \frac{22}{4}
\]
\[
m < 5.5
\]

Thus, the inequality that represents all possible values of \( m \) is:

\[
m < 5.5
\]

This indicates that the student can ride up to 5.5 miles each day from Tuesday to Friday.