A science teacher has a supply 50% sugar solution and a supply of 80% sugar solution how much of each solution should a teacher mix together to get the 105 mL of 60% sugar solution for an experiment
Let's call the amount of the 50% sugar solution x mL and the amount of the 80% sugar solution y mL.
We know that the total volume is 105 mL. So, we can write the equation:
x + y = 105 .......(1)
We also know that the resulting mixture will be 60% sugar solution. Therefore, the amount of sugar in the 50% solution (0.5x) plus the amount of sugar in the 80% solution (0.8y) divided by the total volume (105 mL) should equal 60%. Stated mathematically:
(0.5x + 0.8y) / 105 = 0.6 .......(2)
To solve this system of equations, we can multiply equation (2) by 105 to eliminate the denominator:
0.5x + 0.8y = 0.6 * 105
0.5x + 0.8y = 63 .......(3)
Now we have a system of linear equations:
x + y = 105 .......(1)
0.5x + 0.8y = 63 .......(3)
We can solve this system by substitution or elimination method. Let's use the elimination method:
Multiply equation (1) by 0.5 to make the coefficients of x the same:
0.5x + 0.5y = 0.5 * 105
0.5x + 0.5y = 52.5 .......(4)
Now we can subtract equation (4) from equation (3) to eliminate x:
(0.5x + 0.8y) - (0.5x + 0.5y) = 63 - 52.5
0.8y - 0.5y = 10.5
0.3y = 10.5
y = 10.5 / 0.3
y = 35
Now, substitute the value of y = 35 back into equation (1) to solve for x:
x + 35 = 105
x = 105 - 35
x = 70
So the science teacher should mix 70 mL of the 50% sugar solution with 35 mL of the 80% sugar solution to get 105 mL of a 60% sugar solution for the experiment.