Etch clean graphics uses on cleanser that is 25% acid and a 2ND that is 50% acid. How many liters of each should be mixed to get 30L of a solution that is 40% acid?
amount of the 25% used --- x L
amount of the 50% used --- 30-x L
.25x + .5(30-x) = .4(30)
25x + 50(30-x) = 40(30) ----> (don't like decimals)
solve for x
x is 10 is that the answer and will you explain how you set up the equation
To find the amount of each cleanser needed to achieve a 40% acid solution, we can set up a system of equations based on the acid percentages and quantities.
Let's denote:
x = liters of the 25% acid cleanser
y = liters of the 50% acid cleanser
Based on the given information, we have the following equations:
Equation 1: The total volume of the solution is 30L
x + y = 30
Equation 2: The acid content in the solution will be 40%
0.25x + 0.50y = 0.40(30)
Simplifying Equation 2:
0.25x + 0.50y = 12
Now we can solve the system of equations to find the values of x and y.
Using Equation 1, we can rearrange it to solve for x:
x = 30 - y
Substituting this into Equation 2:
0.25(30 - y) + 0.50y = 12
Expanding and simplifying:
7.5 - 0.25y + 0.50y = 12
0.25y = 12 - 7.5
0.25y = 4.5
y = 4.5 / 0.25
y = 18
Substituting the value of y back into Equation 1:
x + 18 = 30
x = 30 - 18
x = 12
Therefore, to get 30L of a solution that is 40% acid, you should mix 12 liters of the 25% acid cleanser with 18 liters of the 50% acid cleanser.
To solve this problem, we can use a mixture equation based on the amount of acid in each cleanser. Let's assume x liters of the 25% acid cleanser are mixed and y liters of the 50% acid cleanser are mixed.
The equation for the total amount of acid in the mixture is:
0.25x + 0.50y = 0.40(30)
Simplifying the equation, we have:
0.25x + 0.50y = 12
Since we have two unknowns, we need another equation to solve for x and y. The second equation comes from the fact that we need to mix a total of 30 liters:
x + y = 30
Now we have a system of two equations:
0.25x + 0.50y = 12 (Equation 1)
x + y = 30 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use the substitution method in this case.
Rearrange Equation 2 for x:
x = 30 - y
Substitute this value of x into Equation 1:
0.25(30 - y) + 0.50y = 12
Now we can solve for y:
7.5 - 0.25y + 0.50y = 12
0.25y = 12 - 7.5
0.25y = 4.5
y = 4.5 / 0.25
y = 18
Now substitute the value of y back into Equation 2 to solve for x:
x + 18 = 30
x = 30 - 18
x = 12
So, we need 12 liters of the 25% acid cleanser and 18 liters of the 50% acid cleanser to get a 30L solution that is 40% acid.