Melanie needs 75% of sugar solution to conduct an experiment.However she only has 40% and90% sugar solution available .how much each solution must she use in order to obtain 60L of the75% of solution?
Please answer now , it's very important!!
Try making a chart
x + y = 60
.4 x + .9 y = .75 (60)
To find out how much of each solution Melanie needs to obtain 60L of a 75% sugar solution, we can set up a system of equations.
Let's assume Melanie needs x liters of the 40% sugar solution and y liters of the 90% sugar solution.
Since the desired solution is 75% sugar, the total amount of sugar in the mixture will be 60L * 75% = 45L.
Now, let's set up the equation for the total amount of sugar in the mixture:
0.4x + 0.9y = 45 (equation 1)
We also know that the total volume of the mixture is 60L:
x + y = 60 (equation 2)
Now, we can solve these equations simultaneously to find the values of x and y.
One way of doing this is by applying the method of substitution. We can solve equation 2 for one variable (say x) in terms of the other variable (y):
x = 60 - y
Now substitute this expression for x in equation 1:
0.4(60 - y) + 0.9y = 45
Simplify the equation:
24 - 0.4y + 0.9y = 45
Combine like terms:
0.5y = 21
Divide both sides by 0.5:
y = 42
Now, substitute the value of y back into equation 2 to find x:
x + 42 = 60
x = 18
Therefore, Melanie needs 18 liters of the 40% sugar solution and 42 liters of the 90% sugar solution to obtain 60 liters of a 75% sugar solution.