SOLUTION: A hair dye is made by blending a 7% hydrogen peroxide solution and a 4% hydrogen peroxide solution. How many milliliters of each are used to make a 300-millilter solution that is 5
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Question 74740This question is from textbook Introductory Algebra
: A hair dye is made by blending a 7% hydrogen peroxide solution and a 4% hydrogen peroxide solution. How many milliliters of each are used to make a 300-millilter solution that is 5% hydrogen peroxide? This question is from textbook Introductory Algebra
You can put this solution on YOUR website! Let x=amount of 7% solution
Then 300-x=amount of 4% solution
Now we know that the pure hydrogen peroxide that exists before things are mixed together must equal the amount of pure hydrogen peroxide that exists after things are mixed together. So our equation to solve is:
0.07x+0.04(300-x)=0.05(300) get rid of parens
0.07x+12-0.04x=15 subtract 12 from both sides
0.07x+12-12-0.04x=15-12 collect like terms
0.03x=3 divide both sides by 0.03
x=100 ml of 7% solution is needed
300-x=300-100=200 ml of 4% solution is needed
CK
0.07(100)+0.04(300-100)=0.05(300)
7+8=15
15=15
Another way to solve this problem would be:
Let x=amount of 7% solution
Then y=amount of 4% solution
Now we are told that:
x+y=300----------------------------eq 1
note: y=300-x
We are also told that
0.07x+0.04y=0.05(300)--------------------eq 2 multiply eq 2 by 100
7x+4y=1500--------------eq2
substitute y=300-x from eq 1 into eq 2
7x+4(300-x)=1500 get rid of parens
7x+1200-4x=1500 subtract 1200 from both sides
3x=300 divide both sides by 3
x=100 ml of 7%
y=300-x=200 ml of 4%
