Difficulty: Easy

Average Score: 100%

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 equally into twelve 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 the monthly payment amount (a) under the financing offer. This equation accounts for the down payment and the total monthly payments over the course of one year.

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

This equation incorrectly suggests that the total purchase price is derived by first subtracting the down payment from the monthly payment amount, which is not how the financing structure works. The monthly payment should be multiplied by 12 and then added to the down payment to find the total price.

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

This option implies that the purchase price is a fraction of the monthly payment, which is incorrect. The monthly payment is part of the total price, not the other way around, and does not involve dividing the payment by 12 or subtracting the down payment.

C (s = 12a + 50) CORRECT

This is the correct equation. It correctly states that the total purchase price (s) equals twelve times the monthly payment (a) plus the initial down payment of $50. This accurately reflects how the financing plan is structured.

D (s = 12a - 50) YOUR ANSWER

This choice incorrectly suggests that the down payment is subtracted from the total monthly payment contributions. The total price should include the down payment, not deduct it from the payments made over the year.

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

This equation implies that the monthly payment is inclusive of the down payment, which is not accurate. The down payment is a separate initial payment, and the total price should not be calculated by adding the down payment to the monthly payment before multiplying by 12.

Conclusion

The financing offer from the home improvement store clearly indicates that the purchase price is a function of the monthly payments and the initial down payment. The equation s = 12a + 50 correctly summarizes this relationship, ensuring that both the monthly payments and the down payment are accounted for in the total price. Understanding this relationship is crucial for consumers to effectively manage their finances when making significant purchases.