36. A home improvement store offers to finance the purchase of any single item with zero interest for one year, with a down payment of $50. The remainder of the purchase price will be split into 12 equal monthly payments. Which of the following equations represents the relationship between an item's purchase price, s dollars, and the amount, a dollars, of each monthly payment under this offer?
Answer: C
s = 12a + 50
The equation that accurately represents the relationship between an item's purchase price, s dollars, and the amount, a dollars, of each monthly payment is s = 12a + 50. This reflects the total cost comprising the sum of the monthly payments and the initial down payment.
A) s = a-50/12
This equation incorrectly suggests that the monthly payment is reduced by a fraction of the down payment, failing to account for the full relationship defined by the total purchase price and the monthly payments. It misrepresents how the down payment affects the overall cost.
B) s = a/12 -50
This option incorrectly implies that the purchase price is derived from dividing the monthly payment by 12 and then subtracting the down payment. This does not accurately represent the financing structure since the monthly payment is not divided in this manner.
C) s = 12a + 50
This equation correctly captures the relationship, as it indicates that the total purchase price s is equal to the total of 12 multiplied by the monthly payment a, plus the down payment of $50. This is consistent with the financing terms offered by the home improvement store.
D) s = 12a - 50
This option incorrectly suggests that the down payment is subtracted from the total cost of the monthly payments. It does not represent the actual financing structure, which requires the down payment to be added to the total of the monthly payments.
E) s = 12(a + 50)
This equation incorrectly implies that the monthly payment includes the down payment, which is not the case. The down payment is a separate initial cost and should be added to the total of the monthly payments, not included within each monthly payment.
Conclusion
The correct equation s = 12a + 50 accurately reflects the relationship between the total purchase price and monthly payments, incorporating the $50 down payment correctly. All other options misinterpret the financing structure, either by misplacing the down payment or altering the relationship between the monthly payments and total cost.