To find out how many milliliters of pure alcohol should be added to 45 milliliters of an 8% alcohol solution to produce a solution that is 10%, follow these steps:
1. Determine the amount of pure alcohol in the original solution:
- The original solution is 45 milliliters and it is 8% alcohol.
- The amount of pure alcohol in the original solution can be calculated as:
[tex]\[
0.08 \times 45 = 3.6 \text{ milliliters}
\][/tex]
2. Set up the equation:
- Let [tex]\( x \)[/tex] be the amount of pure alcohol to be added.
- After adding [tex]\( x \)[/tex] milliliters of pure alcohol, the new amount of pure alcohol will be [tex]\( 3.6 + x \)[/tex] milliliters.
- The total volume of the new solution will be [tex]\( 45 + x \)[/tex] milliliters.
- We want this new solution to be 10% alcohol. Therefore, we need to solve the following equation:
[tex]\[
\frac{3.6 + x}{45 + x} = 0.10
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Start by multiplying both sides of the equation by [tex]\( 45 + x \)[/tex] to clear the fraction:
[tex]\[
3.6 + x = 0.10 \times (45 + x)
\][/tex]
- Simplify the right-hand side:
[tex]\[
3.6 + x = 4.5 + 0.10x
\][/tex]
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
3.6 + x = 4.5 + 0.10x
\][/tex]
[tex]\[
x - 0.10x = 4.5 - 3.6
\][/tex]
[tex]\[
0.90x = 0.9
\][/tex]
[tex]\[
x = \frac{0.9}{0.90} = 1
\][/tex]
So, the number of milliliters of pure alcohol that should be added is [tex]\( \boxed{1} \)[/tex] milliliter.
