Step 1 :First, we need to understand the problem. John has $100 in his bank account and he earns $4200 per day from his job which he deposits in his bank account.
Step 2 :We are asked to find out how much money he will have after x days and after 10 days.
Step 3 :Let's denote the amount of money John has in his bank account after x days as M(x).
Step 4 :Since John earns $4200 per day and he starts with $100, we can express M(x) as follows: \( M(x) = 100 + 4200x \)
Step 5 :This equation tells us that to find out how much money John has after x days, we just need to multiply 4200 by the number of days and add 100.
Step 6 :Now, let's calculate how much money John will have after 10 days. We substitute x with 10 in the equation: \( M(10) = 100 + 4200*10 \)
Step 7 :After calculating the above expression, we get: \( M(10) = 100 + 42000 = 42100 \)
Step 8 :So, John will have $42100 in his bank account after 10 days.
Step 9 :To check our solution, we can substitute x with 10 in the original equation and see if we get the same result: \( 100 + 4200*10 = 42100 \)
Step 10 :Since the result is the same, our solution is correct.
Step 11 :So, the amount of money John has in his bank account after x days is given by the equation \( M(x) = 100 + 4200x \) and after 10 days he will have $42100.