Mr. Niles has a box of accessories for clarinets. He has a total of 42 objects. He has 12 mouthpieces. He has four times as many reeds as neck straps. How many of each object does he have? I tried so hard but I just didn't understand it and I am in fifth grade. Please answer me as soon as you can Thank you!!!

42 objects - 12 mouthpieces

= 30 objects left consisting of reeds and neckstraps

4 times as many reeds as neckstraps
think of it as 5 groups, 4 are reeds and 1 of nexkstraps

so divide 30 by 5 to get 6 per part.

4 of those parts = 24
1 of the parts = 6

so reeds = 24
neckstraps is 6
mouthpieces = 12

Check to make sure my answer fits all the conditions. It does.

Yat

g=6

12+4x=42. X=15/2

Don't worry, I'm here to help! Let's break down this problem together.

We are given some information about Mr. Niles' collection of clarinet accessories. He has a total of 42 objects, with 12 of them being mouthpieces. We also know that he has four times as many reeds as neck straps.

Let's start by assigning variables to the unknown quantities we are trying to find. Let's say the number of neck straps is "n" and the number of reeds is "r".

We know that Mr. Niles has a total of 42 objects, so we can write an equation based on that:
12 (mouthpieces) + n (neck straps) + r (reeds) = 42.

We also know that Mr. Niles has four times as many reeds as neck straps, which can be written as: r = 4n.

Now we can substitute the value of r in terms of n into the first equation:
12 + n + 4n = 42.

Combining like terms, we simplify the equation:
5n + 12 = 42.

Next, we isolate the variable by subtracting 12 from both sides of the equation:
5n = 42 - 12,
5n = 30.

Finally, we solve for n by dividing both sides of the equation by 5:
n = 30 / 5,
n = 6.

Now that we have found the number of neck straps (n = 6), we can substitute this value back into the equation for r:
r = 4n,
r = 4 * 6,
r = 24.

So, Mr. Niles has 6 neck straps and 24 reeds. We already know he has 12 mouthpieces.

To summarize, Mr. Niles has:
- 12 mouthpieces
- 6 neck straps
- 24 reeds

I hope this explanation helps you understand how to solve the problem! Let me know if you have any other questions.