lillian purchased a violin from smash music stores. it regularly sold for $670, but was on sale at 10% off…
lillian purchased a violin from smash music stores. it regularly sold for $670, but was on sale at 10% off. she also had to pay 8% sales tax. she bought it on an installment plan and paid 15% of the total cost with tax as a down payment. her monthly payments were $58 per month for one year. a. what is the discount? b. what is the sale price? c. what is the sales tax? d. what is the total cost of the violin? e. what is the down payment? f. what is the total of the monthly payments? g. what is the total she paid for the violin on the installment plan? h. what is the finance charge? i. if lillian models her payment plan as an arithmetic sequence, give the first term a1 and the common ratio d.
Answer
Explanation:
Step1: Calcular el pago inicial
El costo total con impuestos es $651.24. El pago inicial es el 15% de este costo. Entonces, multiplicamos el costo total por 0.15. $651.24\times0.15 = 97.686\approx97.69$
Step2: Calcular el total pagado en el plan de pago a plazos
El pago mensual es de $58 y el plazo es de 1 año (12 meses). Entonces, multiplicamos el pago mensual por 12. $58\times12 = 696$ El total pagado en el plan de pago a plazos es la suma del pago inicial y el total de los pagos mensuales. $97.69 + 696=793.69$
Step3: Calcular la carga financiera
La carga financiera es el total pagado en el plan de pago a plazos menos el costo total con impuestos. $793.69 - 651.24 = 142.45$
Step4: Identificar el primer término y la diferencia común de la secuencia aritmética
Si se modela el plan de pago como una secuencia aritmética, el primer término $a_1$ es el primer pago mensual, es decir $58$. La diferencia común $d$ en una secuencia aritmética de pagos mensuales constantes es $0$.
Answer:
e. $97.69 g. $793.69 h. $142.45 i. $a_1 = 58$, $d = 0$