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 36,000 - (5,000 + 500m) to represent the size of his debt after m months. Which number describes the value of his signing bonus? a) 36,000 b) 5,000 c) 500 show your work.
To find the value of his signing bonus, we need to determine the coefficient of the term involving "m".
The expression 36,000 - (5,000 + 500m) represents the size of his debt after m months.
The term involving "m" is 500m.
Since he puts the entirety of his bonus towards paying off his debt, the coefficient of the term involving "m" represents the value of his signing bonus.
Therefore, the value of his signing bonus is 500.
The correct answer is c) 500.
Are you sure the answer is c) 500 and not b) 5,000 which I got as my answer.
Apologies for the previous incorrect response. You are correct, the value of his signing bonus is indeed b) 5,000.
When we simplify the expression 36,000 - (5,000 + 500m), we get:
36,000 - 5,000 - 500m = 31,000 - 500m
The term -500m indicates that for each month, his debt is reduced by 500 times the number of months. Since he puts aside a fixed amount of money every month to pay off his debt and puts the entirety of his bonus towards it, the value 5,000 represents his signing bonus.
The correct answer is b) 5,000.
To find the value of Michael's signing bonus, we need to analyze the expression 36,000 - (5,000 + 500m), which represents the size of his debt after m months.
Given that Michael puts the entirety of his bonus towards paying off his debt, the term 5,000 in the expression represents his bonus.
Therefore, the number that describes the value of his signing bonus is b) $5,000.
To determine the value of Michael's signing bonus, we need to analyze the expression he constructed:
36,000 - (5,000 + 500m)
The expression represents the size of his debt after m months. Breaking down the expression:
- 5,000 represents the fixed amount of money Michael puts aside each month.
- 500m represents the amount that Michael sets aside each month from his monthly salary (assuming that m represents the number of months).
Now, let's simplify the expression:
36,000 - (5,000 + 500m)
Using the distributive property, we distribute the negative sign to both terms inside the parentheses:
36,000 - 5,000 - 500m
This simplifies to:
31,000 - 500m
From the expression, it's clear that 31,000 represents the remaining debt after taking into account the fixed amount put aside each month, the monthly salary allocation, and the bonus.
Therefore, the value of Michael's signing bonus is not represented in the given expression. None of the options (a) 36,000, (b) 5,000, or (c) 500 describe the value of his signing bonus.