###### Example3.1.6

Shane has saved \(\$2{,}500.00\) in his savings account and is going to start saving \(\$550.00\) per month. Tammy has saved \(\$4{,}600.00\) in her savings account and is going to start saving \(\$250.00\) per month. If this situation continues, how many months later would Shane catch up with Tammy in savings?

Shane saves \(\$550.00\) per month, so he can save \(550m\) dollars in \(m\) months. Counting \(\$2{,}500.00\) already in his account, the amount of money in his account is \(550m+2500\) dollars. Similarly, the amount of money in Tammy's account is \(250m+4600\) dollars. To find when those two accounts will have the same amount of money, we write the equation

Here is the full process:

Checking the solution \(7\) in the equation \(550m+2500=250m+4600\text{,}\) we get:

In summary, Shane will catch up with Tammy in the savings account \(7\) months later.