A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the teacher mix together to get a hundred and five milliliters of sixty percent sugar solution for an experiment
Let x represent the amount (in milliliters) of the 50% sugar solution.
Then 105 - x represents the amount of the 80% sugar solution.
The amount of sugar in the 50% solution is 0.5x, while the amount of sugar in the 80% solution is 0.8(105 - x).
To find the total amount of sugar in the mixture, we add these amounts together: 0.5x + 0.8(105 - x).
We know the resulting mixture should be a 60% sugar solution, so we set up the equation:
0.5x + 0.8(105 - x) = 0.6(105)
0.5x + 84 - 0.8x = 63
0.3x + 84 = 63
0.3x = 63 - 84
0.3x = -21
x = -21 / 0.3
x = -70
Since the volume cannot be negative, we conclude that there is no solution to this problem.