Final answer:
To determine the quantity of vegetables purchased, a system of two equations was established based on the total cost and price per kilogram of berenjenas and patatas for two different weeks. By solving the system through the elimination method, it was found that 3 kg of berenjenas and 10 kg of patatas were purchased each week.
Step-by-step explanation:
To calculate the quantity of vegetables purchased, we can set up a system of equations based on the information provided about the costs of the vegetables per week. Let x represent the kilogram quantity of berenjenas and y represent the kilogram quantity of patatas bought each week.
From the first week we have the following equation based on the total cost paid:
2.7x + 0.7y = 15.1
In the subsequent week, the equation changes due to the new prices:
2x + 1.2y = 18
Now we solve the system of equations using an appropriate method such as substitution or elimination. Assuming we use the elimination method:
Multiply the first equation by 2 and the second by 2.7 to align the coefficients for x:
5.4x + 1.4y = 30.2
5.4x + 3.24y = 48.6
Subtract the first new equation from the second to eliminate x:
(5.4x + 3.24y) - (5.4x + 1.4y) = 48.6 - 30.2
1.84y = 18.4
Divide both sides by 1.84 to find y:
y = 10
Substitute y back into one of the original equations to find x:
2.7x + 0.7(10) = 15.1
2.7x + 7 = 15.1
2.7x = 8.1
Divide both sides by 2.7:
x = 3
Thus the student purchased 3 kg of berenjenas and 10 kg of patatas each week.