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 set up a system of equations.
Let x represent the amount (in mL) of the 50% sugar solution.
Let y represent the amount (in mL) of the 80% sugar solution.
Based on the given information, we have the following equations:
x + y = 105 (equation 1, representing the total volume of the solution)
0.5x + 0.8y = 0.6(105) (equation 2, representing the sugar concentration)
Simplifying equation 2:
0.5x + 0.8y = 63
To solve this system of equations, we can multiply equation 1 by 0.5 to eliminate the x term:
0.5x + 0.5y = 52.5
Now we can subtract this equation from equation 2:
0.8y - 0.5y = 63 - 52.5
0.3y = 10.5
y = 35
Substituting this value of y back into equation 1:
x + 35 = 105
x = 70
Therefore, the teacher should mix 70 mL of the 50% sugar solution and 35 mL of the 80% sugar solution. So, the correct answer is option a) 70 mL of the 50% solution and 35 mL of the 80% solution.