23. Ricardo has two bank accounts. Each month, he will withdraw a certain amount of money from the first account and deposit a different amount of money into the second account. The inequality 8,000 – 200x ? 5,000 + 300x can be solved to find the number of months, x, for which the account has more money than the second account. What is the solution to this inequality?
Answer: D
x ≥ 6
The solution to the inequality 8,000 – 200x > 5,000 + 300x indicates that the number of months, x, must be greater than or equal to 6 for the first account to have more money than the second account.
A) x ≤ 6
This option is incorrect because it suggests that the number of months is less than or equal to 6. However, solving the inequality shows that the first account does not exceed the second account until x is 6 or greater.
B) x ≤ 30
While this option includes a range of values, it is incorrect because it suggests that the first account could be greater than the second account until month 30. The solution shows that the threshold begins at month 6, which does not support the condition of being less than or equal to 30.
C) x ≥ 30
This option is incorrect as it implies that the account balance will only exceed the second account starting from month 30. The inequality solution indicates that the first account starts to have more money than the second account at month 6, far before month 30.
D) x ≥ 6
This option is correct because it aligns with the solution derived from the inequality. It indicates that for x values of 6 and above, the first account surpasses the second account in balance.
Conclusion
The correct answer is x ≥ 6, as it accurately reflects the point at which the first bank account's balance exceeds that of the second account. All other options fail because they either set the threshold too low or too high when the actual solution clearly establishes that the balance comparison starts at month 6.