Prime Factorization Homework Problem 3

[shawonna23]

Homework Statement

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?

Homework Equations

don't have any

The Attempt at a Solution

Insufficient information...need to know the total # of beats. Zero

 

[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!

 

[shawonna23]

i got that part about 1/12 and 1/42 but I don't know how to formulate the equation to include x (when they play together)?

 

[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]

 

[shawonna23]

It makes sense...Thanks for the help!

 

[stanton]

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

 

[shawonna23]

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

 

[stanton]

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

 

[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.

 

[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.