Letizia y Marta han ido de compras en las rebajas la primera ha comprado unos pantalones de $42 y una camisa de $24 y la segunda un suéter de $28 y unos zapatos de $60. despues de aplicar los descuentos Letizia a pagado $50,4 y Marta $64,4. calcular los porcentajes de descuentos aplicados sabiendo que el porcentaje aplicado a los pantalones y al suéter coincidían y el aplicado a la camisa y a los zapatos también.

percentage applied to pants and sweater is 80%, and that applied to shirt and shoes is 70%

Step-by-step explanation:

Question in English

Leticia and Marta have gone Shopping in the sales. The First has bought $ 42 pants and a $ 24 shirt, and the second has bought a $ 28 sweater and $ 60 shoes. After applying the discounts, Leticia has paid $ 50.4 and Marta $ 64.4. Calculate the percentages of discounts applied knowing that the percentage applied to the pants and the sweater matched and that applied to the shirt and shoes as well.

Solution

Leticia = 42 + 24 = 50.4

Marta = 28 + 60 = 64.4

The percentage applied to the pants and the sweater coincided (that is, it is x) and that applied to the shirt and shoes also (that is, it is y)

Thus,

1) 42x + 24y = 50.4

2) 28x + 60y = 64.4

obtaining and in 1 we have

y = 50.4 - 42x / 24

y = 2.1 - 1.75x

Substituting and in 2 we obtain

28x + 60y = 64.4

28x + 60 (2.1 - 1.75x) = 64.4

28x + 126 - 105x = 64.4

126 - 64.4 = 105x - 28x

x = 61.6 / 77

x = 0.8

Substituting x into 1 gives:

42x + 24y = 50.4

42 (0.8) + 24y = 50.4

33.6 + 24y = 50.4

y = 50.4 -33.6 / 24

y = 0.7

Therefore, the percentage applied to pants and sweater is 80%, and that applied to shirt and shoes is 70%