Question
How much water should be added to 1 gallon of pure antifreeze to obtain the solution that is 45% antifreeze
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Answer to a math question How much water should be added to 1 gallon of pure antifreeze to obtain the solution that is 45% antifreeze
Adonis
4.4101 Answers
Step 1: Let \( x \) be the amount of water to add.
Step 2: The total volume of the solution will be \( 1 + x \) gallons.
Step 3: The concentration of antifreeze in the solution is given by:
\frac{1 \, \text{gallon of antifreeze}}{1 + x} = 0.45
Step 4: Solving for \( x \):
1 = 0.45(1 + x)
1 = 0.45 + 0.45x
1 - 0.45 = 0.45x
0.55 = 0.45x
x = \frac{0.55}{0.45}
x \approx 1.222
Answer: Approximately 1.222 gallons of water should be added.
Step 2: The total volume of the solution will be \( 1 + x \) gallons.
Step 3: The concentration of antifreeze in the solution is given by:
Step 4: Solving for \( x \):
Answer: Approximately 1.222 gallons of water should be added.
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