A chemist has a bottle of 1% acid solution and a bottle of 5% acid solution. She wants to mix the two to get 100 mL of a 4% acid solution. How much of each should she use?
x = amount of 1% solution
y = amount of 5% solution
I organized the problem in a table:
SOLUTION AMOUNT TOTAL
1% solution -- x -- .01
5% solution -- y -- .05
4% solution --100-- 4
Now that you have this information, you create a system of equations:
.01x + .05y = 4
x + y = 100
I used the substitution method, by making the second equation equal to y first...
y = -x + 100
.01x + .05 (-x + 100) = 4
When you solve this, x = 25. So, you now know that 25 mL of the 1% solution is being used. Now, let's solve for y:
25 + y = 100
y = 75 mL
~~~~~Our final answer is that there are 25 mL of 1% solution and 75 mL of 5% solution.
To determine the amounts of each solution needed, let's represent:
Let x mL be the volume of the 1% acid solution
Then, (100 - x) mL will be the volume of the 5% acid solution
The equation for the amount of acid in the resulting solution is:
0.01x + 0.05(100 - x) = 0.04(100)
Simplifying the equation:
0.01x + 5 - 0.05x = 4
Combine like terms:
-0.04x = -1
Divide both sides by -0.04:
x = -1 / -0.04
x = 25
Therefore, she should use 25 mL of the 1% acid solution and (100 - 25) = 75 mL of the 5% acid solution.
To find out how much of each solution the chemist should use, we can set up a system of equations based on the information given.
Let's call the amount of 1% acid solution x mL, and the amount of 5% acid solution y mL.
From the information provided, we know that the chemist wants to mix these two solutions to obtain 100 mL of a 4% acid solution. This gives us our first equation:
x + y = 100 (equation 1)
We also know that the chemist wants the final concentration of the acid solution to be 4%. This can be expressed using the concentrations of the two solutions:
(0.01x + 0.05y) / 100 = 0.04
By multiplying both sides of the equation by 100 (to eliminate the denominator), we get:
0.01x + 0.05y = 0.04 * 100
0.01x + 0.05y = 4 (equation 2)
Now, we can solve this system of equations using substitution or elimination.
Let's use the substitution method. Rearrange equation 1 to solve for x:
x = 100 - y
Substitute this expression for x in equation 2:
0.01(100 - y) + 0.05y = 4
1 - 0.01y + 0.05y = 4
0.04y = 3
y = 75
Now, substitute this value of y back into equation 1 to solve for x:
x + 75 = 100
x = 100 - 75
x = 25
Therefore, the chemist should use 25 mL of the 1% acid solution and 75 mL of the 5% acid solution to create 100 mL of a 4% acid solution.