CEMC Euclid, 1999

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

The populations of Alphaville and Betaville were equal at the end of 1995. The population of Alphaville decreased by 2.9% during 1996, then increased by 8.9% during 1997, and then increased by 6.9% during 1998. The population of Betaville increased by $r\%$ in each of the three years. If the populations of the towns are equal at the end of 1998, determine the value of $r$ correct to one decimal place.

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