Nikki noticed that is she stacked her dollar bills in stacks of 6 she had 3 left over, stacks of 8, 7 left over, and stacks of 4, 4 left over. If she knows she has less than 100 dollars, how many bills left if she had stacks of 7??
I think you have a typo
If she stacks them in 4's, she can't have 4 left over.
After you find your typo, do the following
numbers which when divided by 6 leave a remainder of 3 are:
3 9 15 21 27 33 39 45 ....
numbers which when divided by 8 leave a remainder of 7 are:
7 15 23 31 39 47 55 ..
do the same for the case where I think you have a typo.
now look for a number or numbers found in all three rows.
then divide that number by 7 and take the remainder.
To find out how many bills Nikki would have left if she stacked them in stacks of 7, we can use the concept of remainders.
Nikki noticed that when she stacked her dollar bills in stacks of 6, she had 3 left over. This means that the number of dollar bills she has is a multiple of 6 plus 3. In other words, we can write the number of dollar bills as 6n + 3, where n is a whole number.
Similarly, when Nikki stacked her dollar bills in stacks of 8, she had 7 left over. This implies that the number of dollar bills she has can be written as 8m + 7, with m being a whole number.
Lastly, when Nikki stacked her dollar bills in stacks of 4, she had 4 left over. The number of dollar bills can be expressed as 4k + 4, where k is a whole number.
Since Nikki knows she has less than 100 dollars, we can start by trying different values for n, m, and k to see if we get a number less than 100.
Let's try n = 1, m = 1, and k = 1:
For stacks of 6: 6 * 1 + 3 = 9
For stacks of 8: 8 * 1 + 7 = 15
For stacks of 4: 4 * 1 + 4 = 8
Adding these results, we get: 9 + 15 + 8 = 32.
Since 32 is less than 100, we can conclude that Nikki has 32 dollar bills.
To find out how many bills Nikki would have left if she stacked them in stacks of 7, we can use the division algorithm.
Divide 32 by 7:
32 รท 7 = 4 with a remainder of 4.
Therefore, if Nikki had stacks of 7, she would have 4 bills left.