A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can't quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees Rita?
$|x-42.80|=12$
$|x+42.80|=12$
$|x-12|=42.80$
$|x+12|=42.80$
Answer (1)
Define x as the amount of money James has after seeing Rita.
Recognize that James either owes or is owed $12 , leading to two possibilities: x = 42.80 − 12 or x = 42.80 + 12 .
Express the relationship as an absolute value equation: ∣ x − 42.80∣ = 12 .
The equation representing the possible amounts of money James may have is ∣ x − 42.80∣ = 12 .
Explanation
Understanding the Problem Let x be the amount of money James has after he sees Rita. We know James currently has $42.80 . If James borrowed $12 from Rita, he will have to pay her back, so he will have 42.80 − 12 dollars. If Rita borrowed $12 from James, she will have to pay him back, so he will have 42.80 + 12 dollars. Therefore, the amount of money James may have after he sees Rita is either 42.80 − 12 or 42.80 + 12 .
Setting up the Equation We can express the two possible amounts of money James may have as x = 42.80 − 12 or x = 42.80 + 12 . This means that the difference between x and 42.80 is 12 . We can write this as an absolute value equation: ∣ x − 42.80∣ = 12 .
Finding the Equation The equation ∣ x − 42.80∣ = 12 represents the amount of money James may have after he sees Rita.
Examples
Imagine you are managing a small business and need to keep track of your cash flow. You know you have $42.80 in your account, but you can't remember if you owe a supplier $12 or if they owe you $12 . The equation ∣ x − 42.80∣ = 12 helps you determine the possible amounts of money you could have after settling the debt. This type of problem is useful in accounting and personal finance to understand potential financial scenarios.
