Prime Factorization Homework Problem 3

1. Oct 18, 2009

shawonna23

1. The problem statement, all variables and given/known data
In one part of a musical composition, the triangle player in an orchestra plays once every 12 beats. The tympani player plays once every 42 beats. How often do they play together?

2. Relevant equations

don't have any

3. The attempt at a solution
Insufficient information...need to know the total # of beats. Zero

2. Oct 18, 2009

stanton

Try to make an equation based on the information. I don't think the total beat number in unnecessary unless the problem required you to do so.
Now suppose 1 is when they play together at the same time
the one play the triangle player makes is 1/12.
The one play tympani player makes, 1/42
yup. looks good to me. Now Construct an equation that connects 1/12 and 1/42, I think I am doing right, although it has been years since I did this kind of probs. I will post more if I have more info!

Last edited: Oct 18, 2009
3. Oct 18, 2009

shawonna23

i got that part about 1/12 and 1/42 but I dont know how to formulate the equation to include x (when they play together)???

4. Oct 18, 2009

stanton

I am sorry about x. I made a mistake. And I got it! I will tell you how to solve it.
1/12+1/42=54/504=3/28
1/(3/28)=28/3=9.3
so 28/3 is the time when they play together. If it does not make sense, please tell me.
I think the answer should be interpreted like this(I THINK. I am not sure) [for every 9.3 beat, they play together]

5. Oct 18, 2009

shawonna23

It makes sense...Thanks for the help!!

6. Oct 18, 2009

stanton

I am glad it was helpful. I am sorry again to confuse you about x. Have a nice day!

7. Oct 18, 2009

shawonna23

Can you please check my work for post: Prime Factorization Homework Problem 1, 2, and 4??

8. Oct 18, 2009

stanton

OK, I will be delighted to help you. :) I summited my opinion in number 1

9. Oct 18, 2009

LearningMath

My guess at this one:

84.

Here's how I arrived at this answer.

1) There are two instruments, a triangle and a tympani, that play every 12 beats and every 42 beats, respectively.

2) Find the prime factors of the two numbers.

12 = 2 * 2 *3; 42 = 7 * 6 = 7 * 3 * 2

3) Select the appropriate prime factors and multiply them together. This is the tricky part - if there are repeat numbers, circle only the largest group of that number (in this case, the 2*2 from the 12) and/or the first instance of that number (in this case, the 3 factored from the 12).

4) So, the numbers we circled are 2*2*3 (every prime factor from the original #12) and the 7 (factored from the #42). Multiply 2*2*3*7 = 84.

5) Make sure 84 is 1) a common multiple of each number and 2) that it is possible that each instrument beats together - by making a chart to check your work.

Since I'm still learning math (e.g., my name), you should draw out a chart and check my answer.

10. Oct 19, 2009

essecks

Like LearningMath said, all of these problems seem to be prime factorisation problems (hence the name). So you're just looking for common factors in all of the answers.

If you don't know what prime factorization is, you can either check http://www.mathsisfun.com/prime-factorization.html" or ask for help from your teacher (assume they're the person setting these homework problems).

:)

In this particular problem, you need whole beats (you can't play 9.3 beats apart) so I think LearningMath's answer is correct.

Last edited by a moderator: Apr 24, 2017