# Paying the rent

Alignments to Content Standards: A-CED.A.1

A checking account is set up with an initial balance of \$4800, and \$400 is removed from the account each month for rent (no other transactions occur on the account).
1. Write an equation whose solution is the number of months, $m$, it takes for the account balance to reach \$2000. 2. Make a plot of the balance after$m$months for for$m=1,3,5,7,9,11$and indicate on the plot the solution to your equation in part (a). ## IM Commentary This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations. ## Solution 1. Since the account starts with \$4,800 and decreases by \$400 each month, there will be$4800-400m$dollars left in the account after$m$months have passed. The question asks us to set up an equation representing the number of months that pass before this quantity equals 2,000, and so the desired equation is $$4800-400m=2000.$$ 2. The following table collects the relevant data points. $m$(months) 1 3 5 7 9 11 Balance$4800-400m$4400 3600 2800 2000 1200 400 As is found in the table or by solving the equation in part (a), the balance in the account is \$2,000 after 7 months. The point $(7,2000)$, and a dashed line plotting the more general relationship, is indicated in the graph below: 