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?
(x - 200)/10
After the customer paid $200, the remaining balance on the appliance is $(x - 200)$. This remaining amount is then divided into 10 equal installments, meaning that after 5 installments, half of the remaining balance has been paid. Thus, the amount still owed after the 5th installment is exactly $(x - 200)/10$.
This choice suggests that after 5 installments, half of the remaining balance is owed. However, since there are 10 equal installments, after 5 installments, the customer would have paid off half of the remaining amount, which is not reflected in this option.
This option implies that the remaining balance is divided by 5 after 5 installments, which is incorrect. The remaining balance after 5 installments should be calculated based on the total number of installments (10), not 5.
This choice incorrectly assumes that the initial payment and the structure of the installment plan lead to a different calculation of the remaining balance. It does not accurately reflect the division of the remaining balance after 5 of the 10 equal payments.
This option suggests that after 5 installments, the remaining balance is based on an incorrect initial total and payment structure. The calculation does not match the installment plan's terms and misunderstands how much has been paid.
The correct remaining balance after the 5th installment is derived from the initial payment structure and the total number of installments. The remaining balance of $(x - 200)$ is divided by 10 to reflect the equal payments made over the installment plan. Thus, the formula $(x - 200)/10$ accurately captures what is owed after 5 payments, distinguishing it from the other choices that misinterpret the installment calculations.
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