Another math problem...please help me come up with an equation for this problem...?

Question

Hector is performing a chemistry experiment that requires 140 ml of a 30% copper sulfate solution. He has a 25% copper sulfate solution and a 60% copper sulfate solution. How many milliliters of each solution should he mix to obtain the needed solution? I know that the answer is 120 ml of the 25% solution, and 20 ml of the 60% solution, but I can't come up with an equation. Any help you can provide would be very much appreciated.

Thank you all for your help.

Answer 1

We can solve this using a system of equations.

Let x be the volume of the 25% solution. Let y be the volume of the 60% solution.

The sums of the volumes must total 140 ml:

x + y = 140.

The mass of CuS04 in the desired solution must equal the amounts added through the use of both solutions.

30 percent of 140ml gives 42 ml of "pure" copper sulfate solution.

The 25% solution would contribute .25x of "pure" copper sulfate solution. The 60% solution would contribute .60y of "pure" copper sulfate solution, so:

0.25x + 0.60y = 42.

Here is the system:

x + y = 140
0.25x + 0.60y = 42

There are many different ways to solve the system. I'll use substitution here:

x + y = 140, so y = 140 - x

0.25x + 0.6(140 - x) = 42
0.25x + 84 - 0.6x = 42
-0.35x = -42
x = 120
y = 20

Since x is the amount of 25% solution and y is the amount of 60% solution, we need 120 ml of 25% solution and 20 ml of 60% solution.

This appears to match your answer!

Answer 2

x+y=140
60x+25y=4200
dividing by 5
12x+5y=840
-5x-5y=-700
adding
7x=140
x=20
sub y=120
add 20 ml of 60% and 120 ml of 25%

Answer 3

30% solution is needed.

so 25x+60y=30(140)
also x+y=140

substitution
x=140-y
25(140-y)+60y=4200
3500+35y=4200
35y=700
y=20ml 60%
x=120ml of 25%

Answer 4

This should be in the chemistry category

Answer 5

same answer as gopal.