How many bottles can you drink? You have 120 bottles of Cola and 120 bottles of Sprite.
You can exchange 3 empty Cola bottles for a new bottle of Sprite.
You can exchange 4 empty Sprite bottles for a new bottle of Cola.
You can borrow bottles, but must return them in the end.
What is the maximal number of bottles of drink that you can drink? Prove the optimality of your result.
As this is a puzzle, please give short and clever answers rather than tedious bruteforce calculations.
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Step-by-step explanation:

You have 120 bottles of Cola and 120 bottles of Sprite.

You can exchange 3 empty Cola bottles for a new bottle of Sprite.

You can exchange 4 empty Sprite bottles for a new bottle of Cola.

You can borrow empty bottles, but must return them in the end.

What is the maximal number of bottles of drink that you can drink? Prove the optimality of your result.

As this is a puzzle, please give short and clever answers rather than tedious bruteforce calculations.

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.