How many quarts of permanent anti-freeze must be added to 10% quarts of a 40% anti-freeze solution in a radiator of a truck to make a 25% anti-freeze solution?
Fix the typo(s)
You cannot add 100% antifreeze to 40% antifreeze and wind up with 25% antifreeze.
Either you are adding water, or you have 10% antifreeze.
To solve this problem, we need to use the concept of mixtures. Let's break down the solution into steps:
Step 1: Understand the problem.
We have two different types of anti-freeze solutions: a 40% anti-freeze solution and a 10% anti-freeze solution. We want to combine them to create a 25% anti-freeze solution. We need to find out how many quarts of the 40% anti-freeze solution we should add to the 10% anti-freeze solution.
Step 2: Assign variables to the unknowns.
Let's assign the following variables:
A = number of quarts of the 40% anti-freeze solution to be added
B = number of quarts of the 10% anti-freeze solution we already have
Step 3: Write the equation based on the problem.
The equation for this problem is:
0.40A + 0.10B = 0.25(A + B)
Step 4: Solve the equation.
Substituting the values, we have:
0.40A + 0.10B = 0.25A + 0.25B
Now, let's simplify the equation:
0.40A - 0.25A = 0.25B - 0.10B
0.15A = 0.15B
Divide both sides of the equation by 0.15:
A = B
This means that the number of quarts of the 40% anti-freeze solution we need to add is equal to the number of quarts of the 10% anti-freeze solution we already have.
Step 5: Calculate the result.
Since A = B, we can substitute A for B in the equation. Let's assume the number of quarts of the 10% anti-freeze solution is x. Therefore, the number of quarts of the 40% anti-freeze solution needed is also x.
So, the answer is x quarts of permanent anti-freeze must be added to x quarts of a 40% anti-freeze solution in a truck radiator to make a 25% anti-freeze solution.