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?

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

Step-by-step 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:

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

This means that:

Together they have 106 students.

This means that:

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

And:

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

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

i only know the sequence of arithmetic it adds the first is 5+4 then it goes up as it adds to then it is 9+5 then 14+6 then to 20+7 and so on. 5,9,14,20,27,35.

step-by-step explanation: