A chemist has a solution that is 70% acid and another that is 45% acid. How many liters of each should he mix to obtain 300 liters of a solution that is 65% acid?
amount of the 70% solution --- x L
amount of the 45% solution--- 300-x L
.70x + .45(300-x) = .65(300)
time 100
70x + 45(300-x) = 65(300
70x + 13500 - 45x = 19500
25x = 6000
x = 240
So 240 L of the 70% stuff, and 60 L of the 45% stuff
check:
.7(240) + .45(60) = 195
.65(300) = 195
looks good to me
To find out how many liters of each solution the chemist should mix, we can solve this problem using a system of equations.
Let's assume that the chemist should mix x liters of the 70% acid solution and y liters of the 45% acid solution.
We have two equations based on the given information:
Equation 1: The total amount of solution is 300 liters, so x + y = 300.
Equation 2: The resulting mixture should be 65% acid, so the amount of acid from the 70% solution plus the amount of acid from the 45% solution should equal 65% of the total amount of solution. Mathematically, this can be expressed as: (0.70x + 0.45y) = 0.65 * 300.
Now, we can solve this system of equations to find the values of x and y.
First, let's rewrite Equation 2 as: 0.70x + 0.45y = 0.65 * 300.
Multiply both sides of Equation 1 by 0.70 to simplify the equation: 0.70x + 0.70y = 0.70 * 300.
Now we have the system of equations:
0.70x + 0.70y = 210
0.70x + 0.45y = 195
Subtract the second equation from the first equation to eliminate x:
(0.70x + 0.70y) - (0.70x + 0.45y) = 210 - 195
0.70y - 0.45y = 15
0.25y = 15
Dividing both sides by 0.25, we find y = 15 / 0.25 = 60.
Substituting this value of y into Equation 1, we can solve for x:
x + 60 = 300
x = 300 - 60
x = 240
Therefore, the chemist should mix 240 liters of the 70% acid solution and 60 liters of the 45% acid solution to obtain 300 liters of a solution that is 65% acid.