Joe vs. Kate's Bank Balances

Statement of the Situation

Joe vs. Kate's Bank Balances over a year.

Identification and Classification of the Variables

Two twins named Joe and Kate start working at the age of 15. Their monthly earnings are \$400 each. Joe starts off with \$350 in his bank account while Kate starts off with \$200. Joe spends \$150 each month(saves \$250) while Kate spends \$100 each month (saves \$300). Their monthly bank balances over the course of a year are shown.

Equations

m = month B= total balance

Joe: B = 250m + 350

Kate: B = 300m + 200

Explanation

The solution of this linear system represents the month that both twins have the same amount of money in the bank. The point of intersection shows that both Joe and Kate have \$1,100 at 3 months. This is the point where Kate catches up to Joe and both now have the same amount of money in the bank. After this point, there is a change and Kate now has a higher bank balance than Joe ( her line is above Joe's). It took three months for Kate to have the same bank balance as Joe, while earning the same amount of money per month but saving different amount. Before this point, Joe had more money in the bank than Kate ( his line was above Kate's).

Summary Statement

Joe starts off with more money than Kate but by saving more each month, Kate catches up to Joe and has the same amount of money ( \$1,100 at 3 months) but then passes Joe and has more money than Joe.