The Scenario: The Powerball Lottery jackpot reaches 1.5 billion dollars, and Jeffrey decides to spend some money each week on lottery tickets. He puts some money in a new bank account and withdrawals the same amount once a week to try his luck at winning the jackpot. After three straight weeks of no luck, Jeffrey has $205 left in his account. After twelve total weeks, he still hasn’t won a thing and has $160 left to spend.
Karen, on the other hand, knows the odds of winning are almost impossible, and decides to start a savings account instead at the same time as Jeffrey. Karen consistently deposits $7 each week into her account, and after seven weeks has a total savings of $89. Unfortunately, Karen’s account does not earn any interest due to the extremely low interest rate.
a) Write an equation that models how much money is in Jeffrey’s account at any given week. Show all work in the space below. You can type your work, or insert a picture of hand-written work.
b) Write an equation that models how much money is in Karen’s account at any given week. Show all work in the space below. You can type your work, or insert a picture of hand-written work
c) Show algebraically when Jeffrey and Karen will have the same amount of money in their accounts. Show all steps.
d) Show algebraically when Jeffrey will run out of money, assuming he never actually wins anything. Show all steps.