How much 10% solution and how much 65% solution should be mixed together to make 100 gal of 35% solution?
Thank you!!
amount of 10% stuff ---- x gal
amount of 65% stuff ---- 100-x gal
solve for x:
.1x + .65x = .35(100)
To determine the quantities of the 10% and 65% solutions needed to make 100 gallons of a 35% solution, we can use the concept of the concentration equation.
Let's represent the amount of the 10% solution as "x" gallons, and the amount of the 65% solution as "y" gallons.
Since the desired total volume of the mixture is 100 gallons, we can express this as an equation:
x + y = 100 (Equation 1)
Now let's consider the concentration of the mixture. The concentration equation can be written as follows:
(Concentration of Solution A * Volume of Solution A) + (Concentration of Solution B * Volume of Solution B) = (Concentration of Mixture * Total Volume of Mixture)
In this case, Solution A refers to the 10% solution, Solution B refers to the 65% solution, and the Mixture refers to the desired 35% solution.
Using the given concentrations, we can rewrite the concentration equation:
(0.10x) + (0.65y) = (0.35 * 100) (Equation 2)
Now we have a system of two equations with two variables. We can solve this system to find the values of "x" and "y".
Let's use the method of substitution to solve the system:
From Equation 1, we can express "x" in terms of "y":
x = 100 - y
Substituting this value of "x" into Equation 2:
(0.10(100 - y)) + (0.65y) = 35
Now we can solve for "y":
10 - 0.10y + 0.65y = 35
0.55y = 25
y = 25 / 0.55
y ≈ 45.45
So, approximately 45.45 gallons of the 65% solution should be mixed with (100 - 45.45) ≈ 54.55 gallons of the 10% solution to create 100 gallons of a 35% solution.
I have a typo, sorry
should be
.1x + .65(100-x) = .35(100)