+103 1. two halls combined have 200 people. if $${\frac{{\mathtt{1}}}{{\mathtt{6}}}}$$ of the people who are in in the first hall will move to the second hall then both of the halls will have the same amount of people inside of them.
1.a. how many people were in both halls at the beginning?
1.b. how many people need to move from the first hall to the second so that the first hall will have *3 more people than the second hall?
1.c. what is the smallest number of people who need to move from the first hall to the second one so that the second hall will have more people than the first one?
+33657 Let the number of people in the first hall be f and the number in the second hall be s.
Then we have
f + s = 200 ...(1)
5f/6 = s + f/6 ...(2) (Because there are 5f/6 people left in the first hall)
From (1) we have s = 200 - f ...(3)
Put this into (2) to get 5f/6 = 200 - f + f/6 or: 5f/6 = 200 - 5f/6 or 10f/6 = 200 so f = 200*6/10 = 120
f = 120
Put this into (3) to get s = 200 - 120 or s = 80
Now see if you can do 1b and 1c yourself. Come back if you still struggle.
+33657 Let the number of people in the first hall be f and the number in the second hall be s.
Then we have
f + s = 200 ...(1)
5f/6 = s + f/6 ...(2) (Because there are 5f/6 people left in the first hall)
From (1) we have s = 200 - f ...(3)
Put this into (2) to get 5f/6 = 200 - f + f/6 or: 5f/6 = 200 - 5f/6 or 10f/6 = 200 so f = 200*6/10 = 120
f = 120
Put this into (3) to get s = 200 - 120 or s = 80
Now see if you can do 1b and 1c yourself. Come back if you still struggle.
