Final answer:
The simplified expression for the amount of money Troy has received from his grandfather and mother after m months is $700 + $40m + $50(m-4).
Step-by-step explanation:
To find the amount of money Troy has received from his grandfather and mother after m months, we need to consider the amounts given by both his grandfather and mother. Troy's grandfather gave him $700 to start his college savings account and also gives him $40 each month. Troy's mother gives him $50 each month but has been doing so for 4 fewer months than Troy's grandfather.
So, the total amount of money Troy has received from his grandfather after m months is $700 + $40m.
And the total amount of money Troy has received from his mother after m months is $50(m-4).
Therefore, the simplified expression for the total amount of money Troy has received from his grandfather and mother after m months is:
$700 + $40m + $50(m-4)