Question 40

s = 12a + 50

The equation that 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 equation correctly accounts for the total monthly payments added to the down payment.

A) s = (a - 50)/12

This equation incorrectly suggests that the monthly payment amount is first reduced by the down payment before being divided by 12. This misrepresents the financing terms, as the down payment is not deducted from the monthly payments but is an upfront cost.

B) s = a/12 - 50

This option implies that the total purchase price is a fraction of the monthly payment minus the down payment, which is incorrect. The monthly payment is actually calculated based on the remaining balance after the down payment, not as a reduction from it.

C) s = 12a + 50

This is the correct equation as it correctly depicts the total purchase price (s) as the sum of twelve monthly payments (12a) plus the initial down payment of $50. It accurately reflects how the financing structure works.

D) s = 12a - 50

This equation inaccurately suggests that the total purchase price is twelve times the monthly payment minus the down payment. This is incorrect because the down payment is an addition to the total, not a deduction from it.

E) s = 12(a + 50)

This option implies that the monthly payment includes the down payment added to it, which leads to an incorrect total price calculation. The down payment is a separate upfront cost and does not contribute to the monthly payment amount directly.

Conclusion

The equation s = 12a + 50 accurately reflects the financing arrangement described in the extract, where the total purchase price is derived by summing the total of the monthly payments and the down payment. All other options misrepresent either the relationship between the monthly payments and the total price or the role of the down payment, making them incorrect.