For a experiment, Jenna needs to make a dilute solution that is 10 ounces of 40% acid. But Jenna only has solutions that are 30% acid and 70% acid. How many ounces of 70% acid solutions should she use?
A. 2.5 ounces
B. 5 ounces
C. 7.5 ounces
D. 8 ounces
Not sure if I would times the ounces with the acid.
To solve this problem, we need to use the concept of mixing two solutions to create a desired concentration. In this case, Jenna needs to make a dilute solution that is 10 ounces in volume and contains 40% acid.
To determine how many ounces of the 70% acid solution Jenna should use, we can set up the following equation:
(30%(x ounces) + 70%(y ounces)) / (x ounces + y ounces) = 40%
Here, x represents the number of ounces of the 30% acid solution and y represents the number of ounces of the 70% acid solution that Jenna needs to use.
We know that the total volume of the resulting solution should be 10 ounces, so we can write:
x ounces + y ounces = 10 ounces
Now, we have a system of equations:
30%(x ounces) + 70%(y ounces) = 40%(10 ounces)
x ounces + y ounces = 10 ounces
We can solve this system of equations using substitution or elimination. In this case, let's solve it using substitution.
From the second equation, we can write:
x ounces = 10 ounces - y ounces
Substitute this expression for x in the first equation:
30%(10 ounces - y ounces) + 70%(y ounces) = 40%(10 ounces)
Now, we can simplify the equation:
0.3(10 - y) + 0.7y = 4
Expand and simplify:
3 - 0.3y + 0.7y = 4
0.4y = 1
y = 1 / 0.4
y = 2.5
Therefore, Jenna should use 2.5 ounces of the 70% acid solution.
Answer: A. 2.5 ounces