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?

Rationale

s = 12a + 50.

The equation s = 12a + 50 accurately represents the relationship between the item's purchase price (s) and each monthly payment (a) after a $50 down payment. This equation accounts for the total cost being made up of the total payments over 12 months plus the initial down payment.

A (s = a-50/12) YOUR ANSWER

This equation incorrectly suggests that the total purchase price is derived from a single monthly payment minus a fraction of the down payment. The structure does not reflect the correct relationship, as it does not account for all monthly payments or the total amount financed.

B (s = a/12 -50) YOUR ANSWER

This equation implies that the purchase price is one-twelfth of the monthly payment minus the down payment. This relationship is incorrect because it misrepresents how the total purchase price is calculated based on the monthly payments made over the financing period.

C (s = 12a + 50) CORRECT

This equation correctly represents the total purchase price, s, as the sum of the total of the 12 monthly payments (12a) plus the initial down payment of $50. This accurately reflects the financing terms of the offer.

D (s = 12a - 50) YOUR ANSWER

This equation suggests that the purchase price is the total of the monthly payments minus the down payment, which is incorrect. The down payment is an upfront cost that should be added to the total of the monthly payments rather than subtracted from it.

E (s = 12 (a + 50)) YOUR ANSWER

This equation miscalculates the relationship by implying that each monthly payment includes an additional $50. This does not represent the financing terms, which separate the down payment from the monthly payments.

Conclusion

The relationship between the total purchase price and the monthly payments is correctly expressed as s = 12a + 50, indicating that the total cost includes the accumulated monthly payments plus the initial down payment. Understanding this equation is crucial for evaluating financing offers accurately.