Question

Mr. Pinter's class has twice as many students as Mrs. Rupert's class. Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class. Together they have 106 students. How many are in each class?

Answer 1

Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.

Explanation:

This question is solved using a system of equations.

I am going to say that:

Mr. Pinter's class has x students.

Mrs. Rupert's class has y students.

Mrs. Althouse's class has z students.

Mr. Pinter's class has twice as many students as Mrs. Rupert's class.

This means that:

`x = 2y`

Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class.

This means that:

`z = 3y - 20`

Together they have 106 students.

This means that:

`x + y + z = 106`

We have x and z has a function of y, so:

`2y + y + 3y - 20 = 106`

`6y = 126`

`y = (126)/(6)`

`y = 21`

And:

`x = 2y = 2(21) = 42`

`z = 3y - 20 = 3(21) - 20 = 63 - 20 = 43`

Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.