Question

Un comerciante tiene dos clases de aceite, la primera de 6 euros el litro y la segunda de 7.2 euros el litro.¿Cuantos litros de cada clase hay que poner para obtener 60 litros de mezcla a 7 euros el litro?

Answer 1

To obtain 60 liters of a 7 euro per liter mixture, the merchant should combine 10 liters of the 6 euro oil with 50 liters of the 7.2 euro oil by solving a system of equations.

Step-by-step explanation:

The question involves a merchant who needs to mix two different types of oil to obtain a 60-liter mixture that costs 7 euros per liter. One type of oil costs 6 euros per liter and the other costs 7.2 euros per liter. To solve this problem, we can use a system of equations.

Let x be the number of liters of the first type (6 euros/liter) and y be the number of liters of the second type (7.2 euros/liter). The total volume of the mixture must be 60 liters, so:

x + y = 60 (Equation 1)

The total cost of the mixture is 7 euros per liter for 60 liters, which equals 420 euros. We can express this with the second equation:

6x + 7.2y = 420 (Equation 2)

We now have a system of two equations with two variables:

• x + y = 60
• 6x + 7.2y = 420

By solving this system, we can find the values of x and y. Multiply Equation 1 by 6:

• 6x + 6y = 360

Subtract this from Equation 2:

• (6x + 7.2y) - (6x + 6y) = 420 - 360
• 1.2y = 60
• y = 50

Substitute y = 50 into Equation 1:

• x + 50 = 60
• x = 10

Therefore, the merchant needs to mix 10 liters of the first type of oil and 50 liters of the second type to get the desired mixture.