Question: Solve the following problems by first formulating an equation in each case:
(a) The sum of twice a number and 5 is equal to the difference between the number and 3. Find the number.
(b) The sum of three successive natural numbers is 10 more than twice the smallest of them. Find the numbers.
(c) Jane receives double pay for every hour she works over and above 38 hours per week. Last week, she worked 48 hours and earned a total of $812. What is Jane's regular hourly wage?
(d) James has invested $15 000 at an annual interest rate of 10%. How much additional money should he invest at the interest rate of 12% if he wants the total interest earned by the end of the year to equal $2100?
(e) When Mr. Barnes passed away, 2/3 of his estate was left to his wife, 1/4 was shared by his children, and the remainder, $100 000, was donated to a charity. How big was Mr. Barnes's estate?