Algebra Question, Please look in Description as question is long

Question

In a strict monastery there are 100 monks, either senior or junior. If a senior monk is allowed to have 3 slices of bread for each meal, and a junior monk is only allowed 1/3 of a slice, and altogether they consume 60 slices of bread during lunch, how many senior monks are there?

Answer 1

S is the number of senior monks.

J is the number of junior monks.

 

S + J = 100

 

3S + J/3 = 60 -->  9S + J = 180  <--- multiplies everything by 3 to clear the fraction 1/3

 

Solving the second equation for J:  J = 180 - 9S

 

Plugging this into the first equation:    S + (180 - 9S) = 100

                                                       180 - 8S  = 100

                                                       180 - 8S - 100 = 0

                                                        80 - 8S = 0

                                                         80 = 8S

                                                         10 = S

 

So there are 10 senior monks and 90 junior monks.

They eat 10*3 + 90(1/3) = 30 + 30  = 60 slices of bread.