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Kelvin and Patrick had some money at a 3:5 ratio. The ratio of their expenses was 3:4. If Kelvin spent 1/3 of his money and Patrick has $55 left, how much money did Kelvin start with?

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$k:p=3:5\\ \frac{1}{3}k:(p-55\ \$)=3:4\\ 5k=3p\\ \underline{\frac{4}{3}k=3p-165\ \$}\\ \frac{11}{3}k=165\ \$$

$k=45\ \$$

$With\ 45\ \$\ did\ Kelvin\ start .$

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