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Hi Jasun, let x represent the number of cars originally in the car park. Since 1/10 x is yellow, x must be divisible by 10. Examples 10, 20, ... 1000.

When 1 is added to x, x + 1, the number must be divisible by 9. Example, 80 + 1 = 81, and 81 is divisible by 9.

One answer is x + 1 = 81.

But that is not the only answer.

All multiples of 80 + n * 90, where n = 0, 1, 2, ...., are multiples which will satisfy the conditions of the question.

Example, n = 3, 80 + 270 = 350.

350 is divisible by 10.

Add 1 to 350 gives 351, which is divisible by 9. 351 / 9 = 39.

Therefore, 351 satisfies the question's requirements also.

Questions?

Perhaps I am reading your solution incorrectly, yet if the starting total is 80 the number of yellows would be 8, 8/80 = 1/10.

If the total increases by one, the fraction is 8/81 ≠ 1/9.

I have dithered with this algebraically, and got inconsistencies.

y/t = 1/10 ⇒ 10y = t

y/(t+1) = 1/9 ⇒ 9y = t + 1

Solving the system for t, 0 = t + 10!

Mark M (not of Bayport)

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