Solution a is 80 percent acid, and solution b is 30 percent acid. How much of each solution is needed to make 200 ml of a solution that is 45 percent acid?
add up the acid amounts. The sum of the parts must equal the whole.
If there are x ml of 80% acid, then the rest (200-x) is 30%. So,
.80x + .30(200-x) = .45*200
Now just crank it out.
To solve this problem, we can set up a system of equations using the information given.
Let's assume "x" represents the amount (in ml) of solution a needed, and "y" represents the amount (in ml) of solution b needed.
From the problem, we know that the total volume of the resulting solution is 200 ml. Therefore, we have the equation:
x + y = 200
We also know that solution a is 80% acid and solution b is 30% acid, and the resulting solution needs to be 45% acid.
So, we can set up the equation based on the acid content as follows:
0.80x + 0.30y = 0.45 * 200
Simplifying the equation, we have:
0.80x + 0.30y = 90
Now we have a system of equations:
x + y = 200
0.80x + 0.30y = 90
To solve this system, we can use the substitution method or the elimination method.
To use the substitution method, we can isolate one variable in the first equation and substitute it into the second equation.
From the first equation, we have:
x = 200 - y
Substituting this into the second equation, we have:
0.80(200 - y) + 0.30y = 90
Simplifying the equation further, we get:
160 - 0.80y + 0.30y = 90
Combining like terms, we have:
-0.50y = 90 - 160
Simplifying, we get:
-0.50y = -70
Dividing both sides by -0.50, we find:
y = 140
Now that we have the value for "y," we can substitute it back into the first equation to find "x."
x + 140 = 200
Subtracting 140 from both sides, we get:
x = 200 - 140
x = 60
Therefore, we need 60 ml of solution a and 140 ml of solution b to make 200 ml of a solution that is 45% acid.
To find the amount of each solution needed, we can set up a system of equations.
Let's assume that we need x ml of solution A and y ml of solution B to make the desired solution.
Given:
Solution A is 80% acid, which means we have 80% of x ml as acid in solution A.
Solution B is 30% acid, which means we have 30% of y ml as acid in solution B.
We can write the following equation for the acid content:
0.80x + 0.30y = 0.45 * 200
Simplifying the equation:
0.80x + 0.30y = 90
To solve this system of equation, we need one more equation. Since we want to make a total of 200 ml of solution, we can add the equation:
x + y = 200
Now we have a system of two equations:
0.80x + 0.30y = 90
x + y = 200
We can solve these equations to find the values of x and y.
1. Let's solve the second equation for x:
x = 200 - y
2. Substitute the value of x in the first equation:
0.80(200 - y) + 0.30y = 90
3. Simplify and solve for y:
160 - 0.80y + 0.30y = 90
-0.80y + 0.30y = 90 - 160
-0.50y = -70
y = -70 / -0.50
y = 140
4. Substitute the value of y back into the equation for x:
x = 200 - 140
x = 60
Therefore, you would need 60 ml of solution A (80% acid) and 140 ml of solution B (30% acid) to make 200 ml of a solution that is 45% acid.