One solution contains 20% acid and a second solution contains 50% acid. How many ounces of each solution should be mixed in order to have 60 ounces of a 30% acid solution?
amount of 20% solution to be used: x ounce
amound of 50% solution to be used : 60-x
.2x + .5(60-x) = .3(60)
time 10
2x + 5(60-x) = 3(60)
2x + 300 - 5x = 180
-3x = -120
x = 40
40 ounce of the 20% and 20 ounces of the 50% solution should be mixed.
Let's assume that x ounces of the 20% acid solution will be mixed and (60 - x) ounces of the 50% acid solution will be mixed.
To find the amount of acid in each solution, multiply the number of ounces by the percentage of acid.
For the 20% acid solution, the amount of acid is 0.2x ounces.
For the 50% acid solution, the amount of acid is 0.5(60 - x) ounces.
To find the total amount of acid in the mixture, it should be equal to 60 ounces multiplied by the desired percentage of acid (30% or 0.3).
So, the equation becomes: 0.2x + 0.5(60 - x) = 0.3 * 60.
Now, let's solve for x:
0.2x + 0.5(60 - x) = 0.3 * 60
0.2x + 30 - 0.5x = 18
-0.3x = -12
x = -12 / -0.3
x = 40
Therefore, you should mix 40 ounces of the 20% acid solution and (60 - 40) = 20 ounces of the 50% acid solution to obtain 60 ounces of a 30% acid solution.
To find the number of ounces of each solution needed to obtain a 30% acid solution, we can use the concept of mixture problems. Here's how to solve it step by step:
Let's assume that x ounces of the 20% acid solution will be mixed with (60 - x) ounces of the 50% acid solution to make a total of 60 ounces of a 30% acid solution.
Since the acid concentration is given as a percentage, we can convert it to a decimal form by dividing it by 100.
Step 1: Set up the equation based on the acid content:
0.20x + 0.50(60 - x) = 0.30(60)
Step 2: Simplify the equation:
0.20x + 30 - 0.50x = 18
Step 3: Combine like terms:
-0.30x + 30 = 18
Step 4: Move constants to the other side:
-0.30x = 18 - 30
-0.30x = -12
Step 5: Solve for x by dividing both sides by -0.30:
x = -12 / -0.30
x = 40
The solution tells us that 40 ounces of the 20% acid solution should be mixed with (60 - 40) = 20 ounces of the 50% acid solution to obtain 60 ounces of a 30% acid solution.