Question

caden was playing with his blocks. he first put all of his blocks into piles of 3 (there was 3 blocks in each pile) but he had 2 blocks left over. he thought that was annoying, so he then tried putting all of his blocks into piles of 6 and again there was 2 left over. he started to get frustrated. he put his blocks in piles of 5, and this time there was 1 left over. He was about to throw his blocks at his sister, Brooklyn, but he decided to try one more time. So finally he put them in piles of 7, and there weren’t any blocks left over. He was estatic and brooklyn was saved! he has fewer than 100 blocks. how many blocks does caden have?

Answer 1

Explanation:

We can use the information provided to set up the following equation:

x = (3n) + 2 = (6n) + 2 = (5n) + 1 = (7n)

We know that n is a positive integer, and x is the total number of blocks.

From the equation, we can see that x is divisible by 3, 6, 5, and 7, but not by 2. Therefore we can use the properties of divisibility to find the number of blocks.

7 is the smallest number that divides x without a remainder. So, we can say that x = 7n, and we can divide both sides by 7:

x/7 = n

We know that x is less than 100, so we can try out different values for n, starting with the smallest.

n = 1, x = 7

n = 2, x = 14

n = 3, x = 21

n = 4, x = 28

n = 5, x = 35

n = 6, x = 42

n = 7, x = 49

n = 8, x = 56

n = 9, x = 63

n = 10, x = 70

n = 11, x = 77

n = 12, x = 84

n = 13, x = 91

n = 14, x = 98

We can see that when n = 14, x = 98. If we were to try for n = 15, x would be 105, which is greater than 100. So, we can conclude that Caden has 98 blocks.