Question

A medium orange has 60 calories and a grapefruit has 80 calories. A citrus gift package contains a total of 12 oranges and grapefruit. The number of calories in the gift package is 780. How many oranges are in the package?

Answer 1

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:

`60x + 80y = 780\\x + y = 12`

From the second equation we have to:

`x = 12-y`

We replace in the first:

`60 (12-y) + 80y = 780\\720-60y + 80y = 780\\720 + 20y = 780\\20y = 780-720\\20y = 60\\y = \frac {60} {20}\\y = 3`

Thus, the package has 3 grapefruits.

On the other hand:

`x = 12-y\\x = 12-3\\x = 9`

Thus, the package has 9 oranges.

Answer:

9 oranges