How much 12% acid must be added to 3 gallons of pure water to get a mixture that is 7% acid.
solve for x, where x is the amount of 12% acid
.12x +0(3) = .07(x+3)
To solve this problem, we need to determine how much 12% acid needs to be added to 3 gallons of pure water to obtain a mixture that is 7% acid.
Step 1: Let's first find the total amount of mixture needed. Since we are adding 12% acid to pure water, the acid content should decrease. Therefore, the total amount of mixture needed is still 3 gallons.
Step 2: Assign variables to the unknowns:
Let x be the amount of 12% acid in gallons that needs to be added.
Step 3: Write the equation based on the acid content:
We can calculate the acid content of the mixture by multiplying the concentration (in decimal form) with the amount (in gallons). The equation is:
0.12x + 0.00(3) = 0.07(3 + x)
Step 4: Solve the equation for x:
0.12x = 0.21 + 0.07x
0.12x - 0.07x = 0.21
0.05x = 0.21
x = 0.21 / 0.05
x = 4.2
Step 5: Answer:
To obtain a mixture that is 7% acid, you need to add 4.2 gallons of 12% acid to 3 gallons of pure water.
To solve this problem, we need to calculate the amount of 12% acid that needs to be added to the pure water. Let's break down the solution step by step.
Step 1: Determine the acid content of the final mixture.
The final mixture should be 7% acid. This means that in every gallon of the mixture, 7% of it should be acid. So, the acid content in the final mixture can be calculated as follows:
Acid content in the final mixture = 7% of the total volume of the mixture
Step 2: Calculate the total volume of the mixture.
We are given that we have 3 gallons of pure water. Let's assume we need to add "x" gallons of 12% acid to it.
Total volume of the mixture = 3 gallons (pure water) + x gallons (12% acid) = 3 + x gallons
Step 3: Set up the equation using the acid content.
Since we know that the acid content in the final mixture should be 7% of the total volume, we can set up the equation as:
Acid content in the final mixture = Acid content in the pure water + Acid content in the 12% acid
Let's substitute the values:
7% of (3 + x) = 0% of 3 + 12% of x
Step 4: Solve the equation for "x".
Now we can solve this equation to find the value of "x", which represents the gallons of 12% acid that need to be added.
(7/100)(3 + x) = (12/100)(x)
0.21 + 0.07x = 0.12x
0.12x - 0.07x = 0.21
0.05x = 0.21
x = 0.21 / 0.05
x = 4.2
Therefore, you would need to add 4.2 gallons of 12% acid to 3 gallons of pure water to obtain a mixture that is 7% acid.