Achemist mixes a 10% hydrogen peroxide solution with a 25% hydrogen peroxide solution to create 30 liters of a 15% hydrogen peroxide solution. how many liters of the 10% solution did the chemist use to make the 15% solution? liters

Let x represent the amount of 10% solution used.
Let y represent the amount of 25% solution used.

Since 30 liters of 15% solution are being made, our first equation is
x + y = 30

Now we deal with the actual peroxide in each solution.
x liters of 10% peroxide contain 0.1x liters of peroxide.
y liters of 25% peroxide contain 0.25y liters of peroxide.
30 liters of 15% peroxide contain 0.15 * 30 = 4.5 liters of peroxide.
From this information, we can write our second equation.

0.1x + 0.25y = 4.5

We have a system of equations:

x + y = 30
0.1x + 0.25y = 4.5

Multiply the first equation by -0.25 and add to the second equation.

-0.25x - 0.25y = -7.5
   0.1x + 0.25y = 4.5

-0.15x              = -3

x = 20

20 liters

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