How many ounces of a $14 \%$ alcohol solution must be mixed with 5 ounces of a $20 \%$ alcohol solution to make a $17 \%$ alcohol solution?
The number of ounces of the $14 \%$ alcohol solution that needs to be mixed is (Simplify your answer.) ounces.
Answer
Final Answer: The number of ounces of the $14 \%$ alcohol solution that needs to be mixed is \(\boxed{5}\) ounces.
Step 1 ：Let x be the amount of the 14% solution. The amount of alcohol in the 14% solution is 0.14x, and the amount of alcohol in the 20% solution is 0.20*5 = 1. The total amount of solution is x + 5 ounces, and the amount of alcohol in this is 0.17*(x + 5).
Step 2 ：We can set up the equation 0.14x + 1 = 0.17*(x + 5) and solve for x.
Step 3 ：The solution to the equation is 5. This means that 5 ounces of the 14% solution must be mixed with the 5 ounces of the 20% solution to make a 17% solution.
Step 4 ：Final Answer: The number of ounces of the $14 \%$ alcohol solution that needs to be mixed is \(\boxed{5}\) ounces.
