Question
Beau had 100 kilograms of a 20% glycol solution. How much of a 30% glycol
solution should he add to get a solution that is 25% glycol?
solution should he add to get a solution that is 25% glycol?
Answers
Answered by
GPT 3.5
Let x be the amount of 30% glycol solution Beau needs to add.
The amount of glycol in the 20% solution is 100 kg * 0.20 = 20 kg.
The amount of glycol in the 30% solution is x kg * 0.30 = 0.3x kg.
The total amount of glycol in the final solution is 20 kg + 0.3x kg.
The total amount of solution is 100 kg + x kg.
To get a 25% glycol solution, the equation is:
(20 kg + 0.3x kg) / (100 kg + x kg) = 0.25.
Multiplying both sides by 100 kg + x kg gives:
20 kg + 0.3x kg = 0.25 * (100 kg + x kg).
Simplifying the right side gives:
20 kg + 0.3x kg = 25 kg + 0.25x kg.
Subtracting 0.25x kg from both sides gives:
20 kg + 0.05x kg = 25 kg.
Subtracting 20 kg from both sides gives:
0.05x kg = 5 kg.
Dividing both sides by 0.05 gives:
x kg = 5 kg / 0.05.
Simplifying the right side gives:
x kg = 100 kg.
Therefore, Beau needs to add 100 kilograms of a 30% glycol solution to get a solution that is 25% glycol.
The amount of glycol in the 20% solution is 100 kg * 0.20 = 20 kg.
The amount of glycol in the 30% solution is x kg * 0.30 = 0.3x kg.
The total amount of glycol in the final solution is 20 kg + 0.3x kg.
The total amount of solution is 100 kg + x kg.
To get a 25% glycol solution, the equation is:
(20 kg + 0.3x kg) / (100 kg + x kg) = 0.25.
Multiplying both sides by 100 kg + x kg gives:
20 kg + 0.3x kg = 0.25 * (100 kg + x kg).
Simplifying the right side gives:
20 kg + 0.3x kg = 25 kg + 0.25x kg.
Subtracting 0.25x kg from both sides gives:
20 kg + 0.05x kg = 25 kg.
Subtracting 20 kg from both sides gives:
0.05x kg = 5 kg.
Dividing both sides by 0.05 gives:
x kg = 5 kg / 0.05.
Simplifying the right side gives:
x kg = 100 kg.
Therefore, Beau needs to add 100 kilograms of a 30% glycol solution to get a solution that is 25% glycol.