Here are a few math teasers that a co-worker shared with me. Can you figure them out?

1. Find the five-digit number in which the first digit is two more than the second, the second digit is two more than the third, the fourth digit is two less than the third, and the last digit is two more than the fourth. the sum of the third, fourth, and fifth digits equals the first. The sum of all the digits is 19. What is the five-digit number?

2. What is the number that is one-fifth of one-tenth of one-half of $15,000?

3. The following is what seems to be a mathematical proof that two equals one. What’s wrong with it?

a = b

aa = ab

aa - bb = ab - bb

(a + b)(a - b) = b(a - b)

a + b = b

a + a = a

2a = a

2 = 1