# Thread: How to find the number of students in three groups when you know the total?

1. ## How to find the number of students in three groups when you know the total?

Hello, I don't know what type of question this is but the homework sheet says 'Parallel questions: Word problems Addition and subtraction'.

The question I'm stuck on is 'There are 70 pupils in total and three clubs. Robotics, Art, and Science. Science has 7 more than art. Robotics has 10 more than science. How many are in the robotics club?'

I understand that art has the fewest, then science, then robotics. Can someone please help, what type of calculation do I do? Is it trial and error? Many thanks.

2. This can be done in several different ways. Trial and error is one; algebra is another; or you could draw a picture and work it out.

Tell us what subject you are learning (and whether you know any algebra); then pick a method to try and take a stab at that method. Once you show some work, we can help you along.

3. You posted this in the Arithmetic sub-forum, so I'm guessing you've not yet learned any algebra. However, we can use some of its principles anyway. One of the most helpful tricks in all of algebra is that we can give names to quantities, even when we don't know the exact value of these quantities. Let's do that now. Let (Robotics) be the number of students in the Robotics Club, (Science) be the number of students in the Science Club, and (Art) be the number of students in the Art Club. We don't know the exact value of any of these numbers, but what do we know? Let's carefully re-read the problem and see what information we can suss out.

There are 70 pupils in total and three clubs, Robotics, Art, and Science.
Aha! This tells us the total number of students across all three clubs. So now we know (Robotics) + (Science) + (Art) = 70. Off to a great start. What else do we know?

Science has 7 more [students] than Art.
Okay, so we know that (Science) = (Art) + 7.

Robotics has 10 more [students] than Science.
Okay, so we know that (Robotics) = (Science) + 10. Hmm... but hold on, we know from earlier that the number of students in Science Club can be written in terms of the number of students in Art Club. Can you use that information to create an equation relating the number of students in Robotics Club to the number of students in Art Club? Finally, can you put everything together to create an equation relating the number of total students (70) to the number of students in Art Club?

Go ahead and give this problem your best efforts. If you get stuck again, that's alright, but when you reply back, please include any and all work you've done on this problem, even the parts you know for sure are wrong. Thank you.

4. Originally Posted by Jonathan99
The question I'm stuck on is 'There are 70 pupils in total and three clubs. Robotics, Art, and Science. Science has 7 more than art. Robotics has 10 more than science. How many are in the robotics club?'
Will you please double-check your typing, to confirm that you typed what you were given? If you did, I think the exercise contains a mistake somewhere.

I tried working the exercise as posted.

I got 22 students in the Science Club.

I got 15 students in the Art Club.

I got 32 students in the Robotics Club.

We cannot have 1/3rd of a student!

5. Hi everyone, thanks for the help. It is 3rd Grade, like a challenge question. The teacher said it wasn't algrebra.
My working was to use drawings, like a bar chart.
One bar for each club. Then +7 for one, and then +7 and +10 for the other. So I got 7+7+10 = 24.
Then I got 70-24 = 46. But I don't do division yet, so needed to share 46 into 3 groups. Doesn't seem to fit. I will check with the teacher.
Many thanks for all the replies and help. I didn't know where to start!

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