An interesting word problem was recently posted at the SingaporeMath Yahoo group. The original poster wrote for help solving it without algebra and mentioned that it was from the Primary 4 books. This seems a little advanced compared to the problems in the text and workbooks. I believe the problem could be from the Challenging Word problems series, which provides answers only.

There are 285 teachers and students in the hall. 5/6 of the students and 1/3 of the teachers went out of the hall. There is an equal number of students and teachers left in the hall. How many teachers were there in the hall at first?

If 5/6 of the students and 1/3 of the teachers went out, there would be 1/6 of the students and 2/3 of the teachers left in the hall.

Begin with the end result:

2/3 of the amount of teachers is equal to 1/6 of the amount of students. For every unit of students, there are 2 units of teachers.

Then let’s work back to how many there were at first:

There are 285 people divided into 15 units.
285 ÷ 15 = 19 people per unit.

There were 3 units of 19, or 57 teachers in the hall at first.

Then, to check out work, let’s find out how many students there were at first.
12 units x 19 people in each = 128 students

128 students + 57 teachers = 285 teachers and students were in the hall at first.

#### How can you extend the problem?

Passionate about Singapore Math + Teacher Trainer and Coach + Treasure Hunter + Learner. Answer to the ultimate question? 42.

1. Sidious says

“12 units x 19 people in each = 128 students”

Do you not mean 228 students? (12 x 19 = 228)

“128 students + 57 teachers = 285 teachers and students were in the hall at first.” ( I think 228 + 57 = 285)

Good otherwise, made me think! 🙂

2. Sidious says

No prob. 🙂

Do not worry, there are 3 types of mathematics experts/fans like us; those that can count/add up and those that can’t! 😛

3. cassyt says

Of course, then there are those of us who proofread incessantly for grammatical mistakes while missing the obvious mathematical ones. 😉

4. Sidious says

LMAO!!! Well… believe it or not, I can spot other people’s mistakes and typo’s, but never my own until it is too late! :-S

5. This is fantastic!!

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