What amount of a 60% acid solution must be mixed with a 30% solution to produce 300 mL of a 45% solution?

amount of 60% stuff --- x ml

amount of 30% stuff ---- 300 - x

.6x + .3(300-x) = .45(300)
.6x + 90 - .3x = 135
.3x = 45
x = 150

150 ml of the 60% solution and 150 ml of the 30% solution

check
.6(150) + .3(150)
= 90+45
= 135 , as needed

To determine the amount of a 60% acid solution needed, let's follow these steps:

Step 1: Assign variables:
Let x be the amount (in mL) of the 60% acid solution needed.

Step 2: Determine the amount of the 30% acid solution needed:
Since we want to end up with a total of 300 mL, the amount of the 30% solution needed can be found by subtracting x from 300 mL. Therefore, the amount of the 30% solution needed is 300 - x mL.

Step 3: Calculate the amount of acid in the 60% solution:
The amount of acid in the 60% solution is 60% of x, which can be written as 0.6x.

Step 4: Calculate the amount of acid in the 30% solution:
The amount of acid in the 30% solution is 30% of (300 - x) mL, which can be written as 0.3(300 - x).

Step 5: Determine the amount of acid in the final solution:
Since we want to end up with a 45% solution, the amount of acid in the final solution is 45% of 300 mL, which can be written as 0.45(300).

Step 6: Write the equation:
Now we can set up the equation:
0.6x + 0.3(300 - x) = 0.45(300)

Step 7: Solve the equation:
0.6x + 90 - 0.3x = 135
0.6x - 0.3x = 135 - 90
0.3x = 45
x = 45 / 0.3
x = 150

Therefore, you need to mix 150 mL of the 60% acid solution with 150 mL of the 30% acid solution to produce 300 mL of a 45% solution.

To solve this problem, we can use a method called the "mixture equation." Here's how to approach it:

Let's assume that x mL of the 60% acid solution needs to be mixed.

Now, let's break down the information we have:

1. The 60% acid solution: Since x mL of this solution is added, the amount of acid in this solution would be 0.6x mL (60% of x).

2. The 30% acid solution: Since we're mixing it with the 60% solution, the amount of acid in this solution would be (300 - x) mL (the remaining volume after removing the added 60% solution). Therefore, the amount of acid in this solution would be 0.3(300 - x) mL (30% of (300 - x)).

To determine the amount of acid in the final 45% solution, we can sum up the amount of acid from both the 60% and 30% solutions:

0.6x + 0.3(300 - x)

Since we want to produce a 300 mL solution with a 45% concentration, the amount of acid in the final solution is given by the equation:

0.6x + 0.3(300 - x) = 0.45 * 300

Now, we can solve this equation to find the value of x (the amount of the 60% acid solution that needs to be mixed):

0.6x + 90 - 0.3x = 135

Combining like terms:

0.3x = 45

Now, divide both sides of the equation by 0.3 to isolate x:

x = 45 / 0.3

x = 150

Therefore, 150 mL of the 60% acid solution must be mixed with 150 mL of the 30% solution to produce 300 mL of a 45% solution.