One of Anne’s most important duties at the clinic is to prepare solutions with the correct amount of anesthetic for animals undergoing surgery. For today’s surgery, she needs 250 milliliters of a 20% solution, but only has a 10% solution and a 60% solution available.
How many milliliters of the 10% solution must Anne mix with the 60% solution to obtain the required solution?
amount of the 10% solution ---- x ml
amount of the 60% solution ---- 250-x ml
.1x + .6(250-x) = .2(250)
times 10
x + 6(250-x) = 2(250)
x + 1500 - 6x = 500
-5x = -1000
x = 200
so 200 ml of the 10% stuff, and 50 ml of the 60% stuff
To find the amount of 10% solution Anne must mix with the 60% solution, we can set up an equation based on the amount of anesthetic required.
Let's assume Anne needs to mix x milliliters of the 10% solution with the 60% solution.
The amount of anesthetic in the 10% solution can be calculated as 0.10x (since it is a 10% solution, meaning it contains 10% anesthetic).
The amount of anesthetic in the 60% solution can be calculated as 0.60(250 - x) (since it is a 60% solution and the total volume is 250 milliliters - x milliliters of the 10% solution).
To obtain the required 20% solution, the total amount of anesthetic from both solutions should equal 20% (0.20) of the total volume (250 milliliters).
So, we can set up the equation:
0.10x + 0.60(250 - x) = 0.20(250)
Simplifying this equation gives us:
0.10x + 150 - 0.60x = 50
Now, we can solve for x:
0.10x - 0.60x = 50 - 150
-0.50x = -100
x = -100 / -0.50
x = 200
Therefore, Anne needs to mix 200 milliliters of the 10% solution with the 60% solution to obtain the required solution.