In the lab, Teresa has two solutions that contain alcohol and is mixing them with each other. She uses
4
times as much Solution A as Solution B. Solution A is
17%
alcohol and Solution B is
10%
alcohol. How many milliliters of Solution B does she use, if the resulting mixture has
234
milliliters of pure alcohol?
a = 4b
.17a + .10b = 234
so,
.78b = 234
b = 300
Let's assume that Teresa uses "x" milliliters of Solution B.
Since she uses 4 times as much Solution A as Solution B, she uses 4x milliliters of Solution A.
Solution A has 17% alcohol, so 0.17 * (4x) = 0.68x milliliters of alcohol come from Solution A.
Solution B has 10% alcohol, so 0.10 * x = 0.10x milliliters of alcohol come from Solution B.
The total amount of alcohol in the final mixture is given as 234 milliliters.
Therefore, 0.68x + 0.10x = 234.
Combining like terms, we have 0.78x = 234.
Dividing both sides by 0.78, we get x = 300.
So, Teresa uses 300 milliliters of Solution B.
To determine how many milliliters of Solution B Teresa uses, we need to set up an equation to represent the total amount of alcohol in the resulting mixture.
Let's say Teresa uses 'x' milliliters of Solution B. Since Solution A is used 4 times as much as Solution B, she uses 4x milliliters of Solution A.
The amount of alcohol in Solution A is 17% of 4x milliliters. This can be written as 0.17 * 4x = 0.68x milliliters.
Similarly, the amount of alcohol in Solution B is 10% of x milliliters, which can be written as 0.10 * x = 0.1x milliliters.
To find the total amount of alcohol in the resulting mixture, we set up the equation:
0.68x + 0.1x = 234
Now, we can solve this equation to find the value of 'x' by combining like terms and isolating 'x':
0.78x = 234
Dividing both sides of the equation by 0.78, we get:
x = 234 / 0.78
Using a calculator, we find that x is approximately 300.
Therefore, Teresa uses 300 milliliters of Solution B.