3. If the higher paid worker's wage is x, the lower paid worker's wage must be x - 2 since their wages are consecutive even integers. Consecutive integers are one number apart; consecutive even integers are two numbers apart since there is one odd number between every two even integers. Summing the two together gives 2x - 2 or 2(x - 1).
4. We can sum terms of an arithmetic sequence (the sum of the terms of an arithmetic sequence is known as an arithmetic series) by using the formula Sn = n * (1/2) * (A1 + An), where n is the number of terms, A1 is the first term, and An is the nth term. There are 21 numbers between 60 and 80, so after plugging in variables we end up with 1470.
5. Another variation of the last formula which is used for summing up the first n integers is Sn = [(n)(n + 1)]/2. This problem is really just asking: "find the smallest n such that 1 + 2 + 3 ... + n is greater than 2000". Since we want our sum to equal 2000, we need to solve the equation 2000 = [(n)(n + 1)]/2. Simplifying, solving for n using the quadratic formula, and discarding the negative solution gives n = ~62.75. Since n is not an integer, we need to look for the first integer which is larger than 62.75, which is 63. Note that this means his can will contain more than 2000 pennies on day 63, but on day 62, it would contain fewer than 2000 pennies.