Michael has substantial student debt, but he recently got a new job, which came with a signing bonus. He calculates that with his new job, he can put aside a fixed amount of money every month to pay off his debt. He also puts the entirety of his bonus towards paying off his debt. He constructs the expression 36,700 - (5,000 + 500m) to represent the size of his debt after m months. Which number describes the value of his signing bonus?
The value of his signing bonus is $5,000.
To determine the value of Michael's signing bonus, we need to solve the expression: 36,700 - (5,000 + 500m) = 0.
We can rearrange the equation to isolate the value of the signing bonus:
36,700 - (5,000 + 500m) = 0
First, let's simplify the expression inside the parentheses:
36,700 - 5,000 - 500m = 0
Next, combine like terms:
31,700 - 500m = 0
Now, move 31,700 to the other side of the equation by adding it to both sides:
-500m = -31,700
To solve for 'm,' divide both sides of the equation by -500:
m = (-31,700) / (-500)
m = 63.4
Therefore, the value of 'm' is 63.4 months.
Since Michael puts the entirety of his bonus towards paying off his debt, the value of his signing bonus can be found by substituting 'm' into the expression:
Signing bonus = 5,000 + 500m
Signing bonus = 5,000 + 500(63.4)
Signing bonus = 5,000 + 31,700
Signing bonus = 36,700
Hence, the value of Michael's signing bonus is $36,700.
To find the value of Michael's signing bonus, we need to rewrite the expression 36,700 - (5,000 + 500m) and isolate the bonus amount.
First, let's simplify the expression by combining like terms:
36,700 - (5,000 + 500m) can be rewritten as:
36,700 - 5,000 - 500m.
Next, let's subtract 5,000 from 36,700:
36,700 - 5,000 = 31,700.
Finally, we can rewrite the expression as:
31,700 - 500m.
From this expression, we can see that 31,700 represents the remaining debt after m months. Therefore, the value of Michael's signing bonus is 31,700 units.