The best way to answer this question is to set up the first sentence as a ratio of large bandages to total bandages. You would write 5 large bandages to 7 total bandages to 7 total bandages. Then you would make this equivalent to x number of large bandages to 60 total. It would look like this 5:7 = x:60. You could use cross products to multiply 60 by 5 to get 300. 7 times x also should equal 300. Unfortunately, this example will not leave us with a whole number of bandages, but 300/7 is a repeating decimal or a mixed number (42 6/7 large bandages).
Find total number of integers.

Find how many integers is divisible by 2.

Eliminate even numbers.
11, 13, 15,..., 57, 59
This array contains 51 - 26 = 25 numbers.
Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.
15, 17, 19,..., 55, 57
This array contains 25 - 3 = 22 numbers.
Now we should eliminate numbers divisible by 3: 15, 21, 27...

There are 8 such numbers.
Therefore, there are 25 - 8 = 17 numbers that <span>can be evenly divided by neither 2 nor 3</span>