# There are 950 students at Hanover High School. The ratio of the number of freshmen to all students is 3:10. The ratio of the number of sophomores to all students is 1:2. What is the ratio of the number of freshmen to sophomores?

Mar 7, 2018

$3 : 5$

#### Explanation:

You first want to figure out how many freshmen there are in the high school. Since the ratio of freshman to all students is $3 : 10$, freshmen represent 30% of all $950$ students, meaning there are

$950 \left(.3\right) = 285$

freshmen. The ratio of the number of sophomores to all students is $1 : 2$, meaning the sophomores represent $\frac{1}{2}$ of all students. So

$950 \left(.5\right) = 475$

sophomores. Since you're looking for the ratio of the number to freshman to sophomores, your final ratio should be $285 : 475$, which is further simplified to $3 : 5$.