Answer:
4 rows
Step-by-step explanation:
First set:
unknown rows, 5 tiles each
meaning old total is divisible by 5
Second set:
3 additional rows, 3 tiles each
meaning that the new total is divisible by 3
so, our total number of tiles is divisible by 5, add 1 and it is divisible by 3 when added 1
{another way I solved it : [and when it is divided by 3, it has 8 that fit into the original pattern; which is another way of knowing that each of the rows of 5 [each have 2 removed when turned into rows of 3] add up to having a remainder of 8 tiles; 8 / 2 = 4; so there were four rows in the original pattern contributing to the change--there were four rows] }
x is divisible by 5, x + 1 is divisible by 3
essentially, we are looking for a number that ends in 5 or 0, and the next number [ending in 6 or 1] is divisible by 3
I know that 5 goes into 20, and that 21 is divisible by 3, so let's test it out:
4 (rows of 5) turns into 7 [4 + 3] rows of 3
because 21 can be split into 7 rows, this number of tiles is possible
so, in the original pattern, there must have been 4 rows
hope this helps!! {so sorry if this confuses you, please let me know if I should explain my reasoning further}
have a lovely day :)
