X : 3C -> 1P + 1A

Y : 3P -> 2C + 1A

It’s been pointed out that from these relations one sees that 300 X operations and 100 Y operations are required. But I think a crucial detail required for the contradiction is missing: for every Y, there must be 3 X’s preceding or else we’d have a negative number of Prii at some time. Thus the last operation must be a Y and so the previous number of Camry’s is -2 which is a contradiction.

At $60 dollars an hour, I wouldn’t ask a lawyer. ðŸ™‚

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We are given:

3C = 1P + 1A

3P = 2C + 1A

(where C = Camry, P = Prius, A = Avalon)

Multiplying the first by 3 gives:

9C = 3P + 3A

Substituting for 3P

9C = 2C + 1A + 3A

7C = 4A

Which gives you exactly 700 to 400 translation. So the answer would be that yes, you can exchange 700 Camrys for 400 Avalons but you need to exchange them in batches of seven.

]]>Borrow 2 Camrys.

3 C, 398 A, 2 P

Exchange 3C for 1 A and 1 P

399 A, 3 P

Trade 3 P for 2 C and 1 A

2 C, 400 A

Return the borrowed Camrys.

400 Avalones.