21. A customer bought an appliance at a purchase price greater than $800 on an installment plan that did not charge any interest. At the time of purchase the customer paid $200 toward the purchase price and then paid the remainder in 10 equal installments. If the purchase price was x dollars what was the amount remaining after the 5th installment?
Answer: C
The amount remaining after the 5th installment is (x - 200)/10.
After the customer paid $200 initially and then made 10 equal installments, the remaining balance after the 5th installment can be calculated by considering how much has been paid and what is left.
A) (x - 200)/2
This option incorrectly suggests that half of the remaining balance after the initial payment has been accounted for. After 5 installments, the customer has actually paid more than half of the total remaining amount, making this option incorrect.
B) (x - 200)/5
This choice implies that the remaining amount is divided by 5, which does not accurately reflect the total payments made or the remaining balance after 5 installments. Since the customer has made multiple payments, this option does not correctly represent the situation.
C) (x - 200)/10
This option accurately represents the remaining balance after the 5th installment. The customer initially paid $200, and with 10 installments, the balance after 5 installments would be correctly calculated as (x - 200)/10, reflecting the amount left to be paid after half of the installments.
D) (x - 400)/5
This option is incorrect because it suggests that $400 has been deducted from the total purchase price, which does not align with the actual payments made. The calculation does not correspond to the installment payment structure provided.
E) (x - 600)/2
This option is also incorrect. It implies an incorrect deduction of $600 from the total purchase price and assumes a division by 2, which does not fit the payment scenario described.
Conclusion
The correct answer, (x - 200)/10, accurately reflects the remaining balance after 5 installments based on the initial payment and total purchase price. All other options misrepresent the payment structure or fail to account for the correct deductions, making them incorrect. Thus, understanding the payment plan is crucial for determining the correct remaining balance.