Hi i need help solving this math problem please

Question

LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50%solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?

Answer 1

Hi Egzona

These are pretty popular problems, and you almost always solve them by figuring out how much undiluted acid (or whatever) there is in each mixture. For instance, if you had 100ml of 30% solution, then 30ml are acid, because 100ml×30%=30ml

In this case, LeBron needs 150 ml of 30% solution. 30% of 150 is 45ml, so he needs 150ml that has 45ml of acid in it.

Let's set some variables for the two solutions that we're mixing. We start with x ml of the 25% solution, and we'll mix it with y ml of the 50% solution. That means the total number of milliliters is x+y. That should be enough to create a system of equations:

x+y=150

0.25x+0.50y=45

The first equation is because we need 150 ml of total solution, the second equation is because the amount of pure, undiluted acid in the solution has to add up to 45 ml.

From here, we're just solving a system of equations. I would recommend elimination, by first doubling the second equation...

x+y=150

0.5x+y=90

... and then subtracting the second equation from the first.

0.5x=60

Solve for x, and we find that we must need 120 ml of the x solution, which was the 25% solution. Go back to either equation to solve for y, and don't forget to check the answer!

Let me know if this needs a different or further explanation.