Plus 1 1 = = Plus 1 % 1\%

Algebra Level 2

Jarex has a mixture of water and alcohol. The concentration of alcohol is 24 % 24\% . He then added 1 1 more liter of alcohol and now the alcohol concentration has increased by 1 % 1\% .

What is the amount of water concentration (in liters)?


The answer is 57.

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1 solution

Kaizen Cyrus
May 20, 2020

Let the mixture (before adding the additional alcohol) be x x . Before adding one liter of alcohol into the mixture, the water concentration was 76 % 76\% . After the addition of alcohol, the water concentration became 75 % 75\% . But its amount never changed since alcohol was only added. We can set up an equality with this information.

76 % of x = 75 % of ( x + 1 ) 19 x 25 = 3 ( x + 1 ) 4 76 x = 75 ( x + 1 ) 76 x = 75 x 75 76 x 75 x = 75 x = 75 \begin{aligned} 76\% \space \text{of} \space x = \space & 75\% \space \text{of} \space (x+1) \\ \frac{19x}{25} = \space & \frac{3(x+1)}{4} \\ 76x = \space & 75(x+1) \\ 76x = \space & 75x-75 \\ 76x-75x = \space & 75 \\ x = \space & 75 \end{aligned}

76 % 76\% of 75 75 liters or 75 % 75\% of 76 76 liters is 57 \boxed{57} liters.

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