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?

Let's use variables.

m = number of morning practices

a = number of afternoon practices

m + a = 10 (there are 10 practices total, either morning or afternoon)

5m + 6a = 57 (each morning practice is 5 hours, afternoon ones are 6. multiply by the number of each and you would get the total number of hours ran, 57)

Let's solve using substitution.

m + a = 10

m = 10 - a

Substitute 10 - a for m.

5 (10 - a) + 6a = 57

50 - 5a + 6a = 57

50 + a = 57

a = 7

Use a = 7 in an earlier equation to find m.

m + a = 10

m + 7 = 10

m = 3

There were 3 morning practices and 7 afternoon practices.