Paying the rent
Task
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).
- Write an equation whose solution is the number of months, $m$, it takes for the account balance to reach \$2000.
- 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
- 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 $$ 4800-400m=2000. $$
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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 Balance in an account 1–11 months after its establishment 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:
Paying the rent
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).
- Write an equation whose solution is the number of months, $m$, it takes for the account balance to reach \$2000.
- 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).