Alab needs a 20 liters of a 15% acid solution. the lab only has a 10% acid solution and a 30% acid solution. how much of the 10% acid solution will they need to mix with the 30% solution to obtain 20 liters of a 15% solution?

To start, it's always easiest to turn percentages into decimals- so let's do that first:

10% Weak solution = .1
30% Strong solution = .3
15% Medium solution = .15

Next we need to assign a value to the amount of each solution we have or need.

Weak solution = x (because we don't yet know how much we need, we give it a variable)
Strong solution= 20-x (because once we determine x and know there are 20 total liters, we can simply subtract to figure out the remainder)
Medium solution= 20 (because in total we need 20 liters)

Now we create the formula to solve for x.

.1x+.3(20-x)=.15(20)
x=15

So you would need 15 liters of the weaker 10% solution and 5 liters of the stronger 30% solution. This makes sense b/c the average 15 is much lower than 30 so we'd expect to need much more of the weaker solution.