Hello, I am stuck on the following problem.(adsbygoogle = window.adsbygoogle || []).push({});

How many milliliters of a 30% acid solution and a 55% acid solution must be mixed to obtain 100 milliliters of a 50% acid solution?

My solution:

Let X = The unknown milliliters of 30% acid.

Let Y = The unknown milliliters of 55% acid.

(1) X + Y = 100

(2) 0.3X + 0.55Y = 0.5

Multiplying (2) by 100 in order to work with integers,

(2) 30X + 55Y = 50

Multiplying (1) by -30 in order to eliminate X

(1) -30X - 30Y = -3000

So our new equations are,

(1) -30X - 30Y = -3000

(2) 30X + 55Y = 50

Adding the two equations in order to eliminate X,

25Y = -2950 => Y = -118

Back-substituting Y in to (1) in order to solve for X,

-30X - 30(-118) = -3000

-30X + 3540 = -3000

-30X = -6540

X = 218

The answer in the book says:

20 milliliters of 30% acid solution and 80 milliliters of 55% acid solution.

Any hints as to where I am going wrong?

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# Homework Help: Systems of equations

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