47. For science class, Kyle needs to make a dilute solution of 12 ounces that is 30% vinegar. But he only has 20% vinegar 60^ vinegar. How many ounces of 20% vinegar should he use?
A. 3 ounces
B. 6 ounces
C. 9 ounces
D. 10 ounces
6 ounces
To solve this problem, we need to understand the concept of dilution and how to calculate it. Dilution is the process of reducing the concentration of a solute in a solution usually by adding more solvent.
We can use the following formula to calculate the dilution:
(C1)(V1) = (C2)(V2)
Where:
C1 = initial concentration of the solute
V1 = initial volume of the solution
C2 = final concentration of the solute (in this case, 30% vinegar)
V2 = final volume of the solution (12 ounces)
Let's solve for V1, which represents the volume of the 20% vinegar we need to use.
We know:
C1 = 20%
C2 = 30%
V2 = 12 ounces
(C1)(V1) = (C2)(V2)
(20%)(V1) = (30%)(12 ounces)
To solve for V1, we can rearrange the equation:
V1 = (30%)(12 ounces) / 20%
V1 = (0.30)(12 ounces) / 0.20
V1 = 3.6 ounces / 0.20
V1 = 18 ounces
So, Kyle needs to use 18 ounces of 20% vinegar to make a dilute solution of 12 ounces that is 30% vinegar.
However, the given options do not include 18 ounces as a choice. We need to find the closest approximation from the given options.
Comparing the given options with the calculated answer, the option closest to 18 ounces is:
D. 10 ounces
Therefore, Kyle should use 10 ounces of 20% vinegar.