The amount of 1% acid solution she needs to mix is 25 ml while the percentage of 5% acid solution she needs to mix is 75 ml.
Given to us
A chemist has a bottle of a 1% acid solution and a bottle of a 5% acid solution.
She wants to mix the two solutions to get 100 ml of a 4% acid solution.
Assumption
Let the amount of 1% acid solution be x ml, and the amount of 5% acid solution be y ml.
Total Amount of the Final Solution
As the chemist wants to mix the two solutions to make 100 ml of solutions, therefore,
amount of 1% acid solution + amount of 5% acid solution = 100ml
x + y = 100.....equation 1
Solving for y,
y = 100 - x
What is the % of the acid in the mixture?
We know that the mixture is having a 4% concentration and is 100 ml in volume.
[tex](1\%)x+(5\%)y = (4\%)100\\0.01x+0.05y=0.04\times 100\\[/tex]
Substitute the value of y,
[tex]0.01x+0.05(100-x)=0.04\times 100\\\\0.01x + (0.05\times 100)-(0.05\times x) = 4\\\\0.01x + 5 -0.05x =4\\\\0.01x-0.05x = 4-5\\\\0.04x = 1\\\\x=\dfrac{1}{0.04}\\\\x = 25\ ml[/tex]
Substitute the value of x in equation y,
[tex]x+y = 100\\25 +y =100\\y = 100-25\\y=75\ ml[/tex]
Hence, the amount of 1% acid solution she needs to mix is 25 ml while the percentage of 5% acid solution she needs to mix is 75 ml.
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