Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money?

We set up a balance equation B(m) where m is the number of months.

Set up Deon's Balance equation:
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 650 - 40m

Set up Mai's Balance equation:
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 850 - 65m

When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m:
650 - 40m = 850 - 65m

Solve for m in the equation 650 - 40m = 850 - 65m

Step 1: Group variables:
We need to group our variables -40m and -65m. To do that, we add 65m to both sides
-40m + 650 + 65m = -65m + 850 + 65m

Step 2: Cancel -65m on the right side:
25m + 650 = 850

Step 3: Group constants:
We need to group our constants 650 and 850. To do that, we subtract 650 from both sides
25m + 650 - 650 = 850 - 650

Step 4: Cancel 650 on the left side:
25m = 200

Step 5: Divide each side of the equation by 25
25m/25 = 200/25
m = 8