1. I assume that you must have full tubes of 5 balls and of 2 balls. I also assume you are looking for the least number of tubes.
To fit the balls in only tubes of 5, you'd need:
62/5 = 12.4, or more than 12 tubes, but fewer than 13.
If you used 12 tubes of 5, you'd fit 60 balls. Then one tube of 3 balls would only have 2 balls.
Try 11 tubes of 5. That fits 55 balls. There are 7 left, but 7 is not divisible by 3.
Try 10 tubes of 5. That fits 50 balls. There are 12 balls left. 12 is divisible by 3.
12/3 = 4.
That means you need 10 tubes of 5 and 4 tubes of 3 to have the smallest number of tubes possible.
2. If you are looking for 2 consecutive integers, then let the smaller integer be x. The larger integer is x + 1.
x + x + 1 = 465
2x + 1 = 465
2x = 464
x = 232
x is the smaller integer, and it is 232. The larger integer is 233.
Here is a way to solve without using an equation learned in algebra.
The sum of the two consecutive integers is 465.
Divide 465/2 = 232.5
Choose one integer just less than 232.5 and one integer just greater than 232.5.
Answer: 232 and 233
