Question

solving problems involving multiple percents continued
6 damon buys lumber worth $562. he gets a 20% contractor’s discount. the sales tax is 6%. his credit card gives him 2% off. how much does he pay?

7 cindy is shopping for a television. the original price is $612. store a has the television on clearance for 30% off. store b has it on clearance for 25% off, and cindy has a 10% off coupon to use at store b. at which store will she pay less? how much less?

8 john goes to a restaurant and has a bill of $32.57. he uses a 10% off coupon on the cost of the meal. the tax is 8%. he leaves a tip of 18% on the amount before the coupon or tax is applied. how much does he spend?

9 explain which situation will give you the best price: a discount of 15% and then 10% off that amount, a discount of 10% and then 15% off that amount, or a discount of 25%.

Explanation:

Problema 6

Step1: Aplicar descuento de contratista

Precio después de 20% de descuento: $562 \times (1 - 0.20) = 562 \times 0.80 = 449.60$

Step2: Aplicar descuento de tarjeta de crédito

Precio después de 2% de descuento adicional: $449.60 \times (1 - 0.02) = 449.60 \times 0.98 = 440.608$

Step3: Aplicar impuesto de ventas

Precio final con impuesto del 6%: $440.608 \times (1 + 0.06) = 440.608 \times 1.06 = 467.04448$

Step1: Calcular precio en Tienda A

Precio después de 30% de descuento: $612 \times (1 - 0.30) = 612 \times 0.70 = 428.40$

Step2: Calcular precio en Tienda B

Primer descuento del 25%: $612 \times (1 - 0.25) = 612 \times 0.75 = 459$
Descuento adicional del 10%: $459 \times (1 - 0.10) = 459 \times 0.90 = 413.10$

Step3: Comparar precios y calcular diferencia

Diferencia: $428.40 - 413.10 = 15.30$

Step1: Calcular descuento de comida

Precio después de 10% de descuento: $32.57 \times (1 - 0.10) = 32.57 \times 0.90 = 29.313$

Step2: Calcular impuesto sobre el precio descontado

Impuesto del 8%: $29.313 \times 0.08 = 2.34504$
Precio con impuesto: $29.313 + 2.34504 = 31.65804$

Step3: Calcular propina sobre precio original

Propina del 18%: $32.57 \times 0.18 = 5.8626$

Step4: Sumar todos los gastos

Gasto total: $31.65804 + 5.8626 = 37.52064$

Answer:

$\$467.04$

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Problema 7