If j is the number of integers between 1 and 500 that are divisible by 9 and k is the number of integers between 1 and 500 that are divisible by 7 what is j+k.
500/9 = 55.5
so there are 55 from 9 to 495
j = 55
500/7 = 71.4
so there are 71 from 7 to 497
k = 71
Well, it seems like we have a math problem on our hands! Let's break it down, shall we?
To find "j," we need to count the number of integers between 1 and 500 that are divisible by 9. Now, all we need to do is find out how many nine-piece chicken nuggets we can fit in a 500-piece bucket, right? Just kidding, let's get back to the math.
We know that 9 times 1 is 9, so the first number that's divisible by 9 is 9. The next one is 18, and so on. Now, we just have to keep counting until we hit 500, right?
Well, not really. We can find the number of integers divisible by 9 between 1 and 500 by dividing 500 by 9. But I'm not great at division, so let me grab my calculator... *drum roll, please* ...It looks like the result is around 55.5555. But since we can't have a fraction of an integer, we'll round down to 55.
So, j is 55! Now, let's find out what k is.
Following a similar approach, we divide 500 by 7 to find the number of integers divisible by 7 between 1 and 500. And after some quick calculation magic, we find that k is approximately 71.4285. But once again, we can't have a fraction of an integer, so we'll round that down to 71.
Now, with all the heavy math lifting done, we can finally find j + k. Simple addition time!
55 plus 71 equals... *drum roll, please* ...126!
So, the answer to your question is 126. I hope my silly explanation brought a smile to your face, even though math might not be the most humorous subject. Keep those brain cells crunching!
To find the value of j, we need to determine how many integers between 1 and 500 are divisible by 9.
Step 1: Find the first multiple of 9 greater than or equal to 1.
Smallest multiple of 9 greater than or equal to 1 is 9.
Step 2: Find the last multiple of 9 less than or equal to 500.
Largest multiple of 9 less than or equal to 500 is 495.
Step 3: Calculate the number of multiples of 9 between 1 and 500.
j = (495 - 9) / 9 + 1
j = 486 / 9 + 1
j = 54 + 1
j = 55
Now, let's find the value of k, which represents the number of integers between 1 and 500 that are divisible by 7.
Step 1: Find the first multiple of 7 greater than or equal to 1.
Smallest multiple of 7 greater than or equal to 1 is 7.
Step 2: Find the last multiple of 7 less than or equal to 500.
Largest multiple of 7 less than or equal to 500 is 497.
Step 3: Calculate the number of multiples of 7 between 1 and 500.
k = (497 - 7) / 7 + 1
k = 490 / 7 + 1
k = 70 + 1
k = 71
Finally, we can find j + k:
j + k = 55 + 71
j + k = 126
Therefore, j + k is equal to 126.
To find the number of integers between 1 and 500 that are divisible by 9 (j), and the number of integers between 1 and 500 that are divisible by 7 (k), we need to find the multiples of 9 and 7 respectively.
Multiples of 9:
To find the multiples of 9, we can start with the first multiple of 9 which is 9 itself. The next multiple of 9 would be 18, then 27, and so on. We keep adding 9 to the previous multiple until we reach a number greater than 500.
9, 18, 27, 36, 45, 54, 63, 72, ...
Since the question asks for the number of integers between 1 and 500 that are divisible by 9, we need to find how many multiples of 9 are less than or equal to 500.
To find this, we divide 500 by 9:
500 ÷ 9 = 55.55...
Since we need the number of integers, we round this answer down to the nearest whole number:
55.55... ≈ 55
So, j = 55.
Multiples of 7:
Similar to finding the multiples of 9, we start with the first multiple of 7 which is 7 itself, then add 7 each time to find the next multiple.
7, 14, 21, 28, ...
To find the number of multiples of 7 less than or equal to 500, we divide 500 by 7:
500 ÷ 7 = 71.42...
After rounding down to the nearest whole number, we get:
71.42... ≈ 71
So, k = 71.
Finally, to find j + k, we simply add the values of j and k.
j + k = 55 + 71 = 126.
Therefore, j + k is equal to 126.