Question

A cross-country team had a total of 10 practices last week, with each practice being in the morning or the afternoon. During each morning practice, they ran 5 miles, and during each afternoon practice, they ran 6 miles. If they ran a total of 57 miles last week, how many morning practices did they have?
3
5
6
7

Answer 1

Let \( m \) be the number of morning practices and \( a \) be the number of afternoon practices. We have the following two equations based on the problem:

1. The total number of practices:
\[
m + a = 10
\]

2. The total miles run:
\[
5m + 6a = 57
\]

We can use the first equation to express \( a \) in terms of \( m \):
\[
a = 10 - m
\]

Now, we can substitute this expression for \( a \) into the second equation:
\[
5m + 6(10 - m) = 57
\]

Expanding this gives:
\[
5m + 60 - 6m = 57
\]

Simplifying this, we get:
\[
-1m + 60 = 57
\]

Now, solving for \( m \):
\[
-1m = 57 - 60
\]
\[
-1m = -3
\]
\[
m = 3
\]

Thus, the number of morning practices \( m \) is \( \boxed{3} \).

To verify, we can find \( a \):
\[
a = 10 - 3 = 7
\]

Now check the miles:
\[
5m + 6a = 5(3) + 6(7) = 15 + 42 = 57
\]

The calculations confirm that the solution is correct, and the number of morning practices is indeed \( \boxed{3} \).