Question

A mixture of Excelsa Coffee and Liberica Coffe costs P 360.00 per kilogram. The Excelsa Coffee costs P 320.00 per kilogram. The Liberica Coffee costs 420.00 per kilogram. How many kilograms o of each are used in the 12kg mixture

Answer 1

To solve the coffee mixture problem, algebraic equations were used to find that the mixture consists of 7.2 kg of Excelsa Coffee and 4.8 kg of Liberica Coffee.

Step-by-step explanation:

The student is asking for help to determine the amount of Excelsa Coffee and Liberica Coffee used in a 12 kg mixture, where the final mixture costs P 360.00 per kilogram. They've provided the costs of the individual coffees: Excelsa Coffee at P 320.00 per kilogram and Liberica Coffee at P 420.00 per kilogram.

To solve this problem, we use the method of algebraic equations. Let x represent the kilograms of Excelsa Coffee and y represent the kilograms of Liberica Coffee used in the mixture. We have two equations based on the information given:

• The sum of the quantities of Excelsa and Liberica coffees is 12 kg: x + y = 12.
• The total cost for the mixture is P 360 per kg for a 12 kg mixture, giving us the equation: 320x + 420y = 360 × 12.

To solve the system of equations, we can use substitution or elimination method. First, from the first equation, we can express y as y = 12 - x. Then, we substitute this into the second equation and solve for x:

• 320x + 420(12 - x) = 4320
• 320x + 5040 - 420x = 4320
• -100x = -720
• x = 7.2

Now that we have the value for x, we can determine y by substituting x back into the equation y = 12 - x:

• y = 12 - 7.2
• y = 4.8

Therefore, the mixture contains 7.2 kg of Excelsa Coffee and 4.8 kg of Liberica Coffee.