For this case we propose a system of equations:
x: Variable representing the amount of oranges
y: Variable that represents the amount of grapefruit
We have to meet a citrus gift package:
[tex]60x + 80y = 780\\x + y = 12[/tex]
From the second equation we have to:
[tex]x = 12-y[/tex]
We replace in the first:
[tex]60 (12-y) + 80y = 780\\720-60y + 80y = 780\\720 + 20y = 780\\20y = 780-720\\20y = 60\\y = \frac {60} {20}\\y = 3[/tex]
Thus, the package has 3 grapefruits.
On the other hand:
[tex]x = 12-y\\x = 12-3\\x = 9[/tex]
Thus, the package has 9 oranges.
Answer:
9 oranges
