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 105 mL of 60% sugar solution for an experiment ? (1 point) Responses 70 mL of the 50% solution and 35 mL of the 80% solution 70 mL of the 50% solution and 35 mL of the 80% solution 35 mL of the 50% solution and 70 mL of the 80% solution 35 mL of the 50% solution and 70 mL of the 80% solution 70 mL of the 50% solution and 70 mL of the 80% solution 70 mL of the 50% solution and 70 mL of the 80% solution 35 mL of the 50% solution and 35 mL of the 80% solution

Answer 1

To solve this problem, we can set up a system of equations.

Let x represent the amount of the 50% sugar solution and y represent the amount of the 80% sugar solution.

We are given two pieces of information:

1) The total volume of the mixture is 105 mL: x + y = 105.

2) The resulting mixture is 60% sugar: 0.5x + 0.8y = 0.6(105).

Now we can solve this system of equations.

From the first equation, we can solve for x: x = 105 - y.

Substituting this expression for x into the second equation, we get:

0.5(105 - y) + 0.8y = 63
52.5 - 0.5y + 0.8y = 63
0.3y = 10.5
y = 35

Substituting this value for y back into the first equation, we can solve for x:

x + 35 = 105
x = 70

So, the teacher should mix 70 mL of the 50% sugar solution and 35 mL of the 80% sugar solution.