# Question #03002

Dec 9, 2017

Use a simultaneous equation.
Barako coffee…$7.2$kg Arabica coffee…$4.8$ kg

#### Explanation:

Let $x$ the mass of the Barako coffee and $y$ the mass of the Arabica coffee. (Unit in kg).

Total 12 kilograms of coffee beans are used.
$x + y = 12$ ・・・[1]

Total cost is $360 \cdot 12 = 4320$ pesos.
$320 x + 420 y = 4320$・・・[2]

To solve [1] and [2], multiple both sides of [1] by $320$.
$320 x + 320 y = 3840$・・・[3]

$\text{ }$ [2] $320 x + 420 y = 4320$
$\text{ -)}$ [3]$320 x + 320 y = 3840$
$\text{ } 100 y = 480$
Therefore,
$y = \frac{480}{100} = 4.8$
and
$x = 12 - 4.8 = 7.2$

So, $7.2$ kilograms of Barako coffee and $4.8$ kilograms of Arabica coffee are used.