At
euclid middle school, of the 30 girls who tried out for the lacrosse team, 12
were selected and of the 40 boys who tried out, 16 were selected. are the ratios of number of students on the
team to number of student trying out the same for both boys and girls? how do you know?

Yes because if you simplify both of the ratios they are equal.

For girls it is 30 to 12, which simplified (divided by 3) is 10 to 4 (divided by 2) is 5 to 2

For boys it is 40 to 16 which simplified (divided by 4) is 10 to 4 (divided by 2) is also 5 to 2. Therefore they are both equal.