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 105mL of 60% sugar solution for an experiment?
a ) 70ml of the 50% solution and 35ml oh the 80% solution
b ) 35 ml of the 50% solution and 70 ml of the 80% solution
c ) 70 ml of the 50$ solution and 70 m of the 80% solution
d ) 35 ml of the 50% solution and 35 ml of the 80$ solution
To solve this problem, we can use the method of alligation.
Let's assume that x mL of the 50% sugar solution is mixed with (105 - x) mL of the 80% sugar solution to get 105 mL of the 60% sugar solution.
Now, let's calculate the amount of sugar in each solution.
For the 50% sugar solution:
Sugar content = 50% of x mL = (50/100)*x = 0.5x
For the 80% sugar solution:
Sugar content = 80% of (105 - x) mL = (80/100)*(105 - x) = 0.8(105 - x) = 84 - 0.8x
Now, we can set up an alligation diagram to determine the ratio of the two solutions:
50% 60% 80%
|_________|_________|
x 105 - x
To find the amount of each solution, we need to determine the position of the 60% sugar solution (middle amount). Since 60% is closer to 50% than 80%, we can deduce that the ratio should be more of the 50% solution than the 80% solution.
From the diagram, we can see that the ratio of the 50% solution to the 80% solution is (105 - x):x = (105 - x)/x.
To find the value of x, we need to equate the ratio with the corresponding ratio of sugar contents:
(105 - x)/x = 0.8(105 - x)/0.5x
Simplifying this equation:
(105 - x)*0.5x = 0.8(105 - x)*x
52.5x - 0.5x^2 = 84x - 0.8x^2
0.8x^2 - 84x + 52.5x - 0.5x^2 = 0
0.3x^2 - 31.5x = 0
0.3x(x - 105) = 0
x = 0 or x - 105 = 0
Since a negative value for x doesn't make sense, we can ignore the x = 0 solution. Thus, we have:
x - 105 = 0
x = 105
This means that we need to mix 105 mL of the 50% sugar solution with (105 - 105) = 0 mL of the 80% sugar solution to get 105 mL of the 60% sugar solution.
Since 105 mL of the 50% solution and 0 mL of the 80% solution does not match any of the given options, we can conclude that none of the options provided in the question are correct.
Therefore, the correct answer is e) None of the options are correct.