Sums I

1. Find the sum of all multiples of 5, from 20 to 200.

2. Find the sum of all integers from 20 to 200 that are multiples of 5 or 7.

Hint 1

Consider just the numbers $20$ to $40$, are there any numbers added multiple times if you add up all multiples of $5$ and all multiples of $7$?

3. Find the sum of all $x$ that solve the equation $2x + 5y = 98,\; x, y \in \mathbb Z^+$.

Hint 1

Find the smallest and largest values of $x$.

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