In a chemistry lab, you have two vinegars. One is 20% acetic acid and one is 50% acetic acid. You want
to make 200 mL of a vinegar with 30% acetic acid. How many milliliters (mL) of each vinegar do you
need to mix together?
https://www.jiskha.com/questions/1783700/Joe-owns-a-sandwich-shop-He-charges-10-00-for-two-sandwiches-and-one-drink-and#1814501
To find out how many milliliters (mL) of each vinegar you need to mix together, you can use the concept of the Mixture Problem. In this problem, you want to determine the quantities of two solutions with different concentrations that you need to mix in order to achieve a desired concentration.
Let's define the following variables:
1. Let x represent the volume of the 20% vinegar that you need to mix.
2. Let y represent the volume of the 50% vinegar that you need to mix.
Now, let's set up an equation based on the concentration of acetic acid in the vinegar and the total volume:
For acetic acid:
0.2x + 0.5y = 0.3(200)
This equation represents the fact that the total amount of acetic acid in the mixture is equal to 30% of the total volume (200 mL).
Next, we need to consider the volume of the mixtures:
x + y = 200
This equation represents the fact that the total volume of the mixture is equal to 200 mL.
Now, we have a system of equations that we can solve to find the values of x and y.
Solving the system of equations:
Rearrange the second equation to express x in terms of y:
x = 200 - y
Substitute this expression for x in the first equation:
0.2(200 - y) + 0.5y = 0.3(200)
Distribute and simplify:
40 - 0.2y + 0.5y = 60
0.3y = 60 - 40
0.3y = 20
y = 20 / 0.3
y = 66.67 mL
Substitute the value of y back into the equation x = 200 - y:
x = 200 - 66.67
x = 133.33 mL
Therefore, to make a vinegar with 30% acetic acid, you need to mix 133.33 mL of the 20% acetic acid vinegar with 66.67 mL of the 50% acetic acid vinegar.