The ratio of the number of junior high students to the number of senior high students in a school is 7 to 9. If there are 100 more senior high students than junior high students, how many junior high students are there?
if there are n jr high students, then we have
n/(n+100) = 7/9
9n = 7(n+100)
2n = 700
n = 350
To find the number of junior high students, we can set up a proportion using the given ratio. Let's represent the number of junior high students as "x" and the number of senior high students as "y".
According to the given information, the ratio of junior high students to senior high students is 7 to 9, which can be written as x/y = 7/9.
We also know that there are 100 more senior high students than junior high students, so y = x + 100.
To solve this problem, we can substitute the value of y from the second equation into the first equation.
x/(x + 100) = 7/9
To eliminate the fractions, we can cross-multiply:
9x = 7(x + 100)
Simplifying the equation:
9x = 7x + 700
Subtracting 7x from both sides:
2x = 700
Dividing both sides by 2:
x = 350
Therefore, there are 350 junior high students in the school.