Pedro compró un minigimnasio para ejercitarse
en casa y mejorar su condición física. En la
compra le hicieron dos descuentos sucesivos del
30% y el 20%. Si ahorró S/ 352, ¿cuánto pagó?

Answer:

Pedro pagó $448

Step-by-step explanation:

Sea P el precio inicial de un objeto.

Si aplicamos un descuento del X%, entonces el nuevo precio del objeto es:

NP = P*(1 - X%/100%)

y lo que estamos ahorrando es:

P - NP

En este caso, primero tenemos un descuento del 30%, entonces:

NP = P*(1 - 30%/100%) = P*(1 - 0.3)

Luego tenemos otro descuento, esta vez del 20%, entonces:

NP' = NP*(1 - 20%/100%) = P*(1 - 0.3)*(1 - 20%/100%) = P*(1 - 0.3)*(1 - 0.2)

Lo que Pedro ahorra es igual a $352

entonces:

P - NP' = $352

P -  P*(1 - 0.3)*(1 - 0.2) = $352

P*(1 - (1 - 0.3)*(1 - 0.2)) = $352

P*(1 - 0.56) = $352

P = $352/(1 - 0.56) = $800

Esto significa que el precio original era $800.

Y lo que pedro pago esta dado por la ecuación:

NP' = P*(1 - 0.2)*(1 - 0.3) = $800*(1 - 0.2)*(1 - 0.3) = $448.

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