Ineed stat plz plz plz betty has between $40$ and $50$ pennies that she wants to arrange in a rectangular array. she notices she can arrange the pennies in three different ways without any gaps or spaces. however, if betty adds two more pennies to her collection, she can only arrange the pennies in one way without any gaps or spaces: a straight line. how many pennies does betty have?

If she adds two pennies, she can only arrange the pennies in a straight line.
A straight line is one penny wide. If she adds two pennies she ends up with a prime number of pennies.

Since she has between 40 and 50 pennies, she can have 41, 42, 43, 44, 45, 46, 47 ,48, or 49  pennies.

41 + 2 = 43 prime
42 + 2 = 44 not prime
43 + 2 = 45 not prime
44 + 2 = 46 not prime
45 + 2 = 47 prime
46 + 2 = 48 not prime
47 + 2 = 49 not prime
48 + 2 = 50 not prime
49 + 2 = 51 not prime

Only 43 and 47 are prime.
That means she has 41 or 45 pennies.
41 is prime, so it cannot be arranged in any other way than a straight line 1 by 41.
Let's look at 45.

45 = 3 * 3 * 5

45 = 9 * 5 = 3 * 15 = 45 * 1

She has 45 pennies.