Question 1154729
<font color=black size=3>
I'm assuming you meant to write "60" instead of "6060". 


Gabe needs 60 liters of the 40% solution. This solution is a mix of water and pure acid. Specifically 60*0.4 = 24 liters of pure acid are needed. 


Let 
x = amount of the 30% solution (in liters)
y = amount of the 60% solution (in liters)


Based on those definitions above, we can say
0.30x = amount of pure acid from the 30% mix
0.60y = amount of pure acid from the 60% mix
0.30x+0.60y = amount of pure acid in total
0.30x+0.60y = 24, since Gabe wants 24 liters of pure acid in the end


At the same time, we can also say x+y = 60 because the two individual solution amounts (x and y) will combine to the overall amount of solution of 60 liters. Solve for y to get y = 60-x


Plug this into 0.30x+0.60y = 24, and solve for x


0.30x+0.60y = 24
0.30x+0.60( y ) = 24
0.30x+0.60( 60-x ) = 24 ... replace y with 60-x
0.30x+0.60(60)+0.60(-x) = 24 ... distribute
0.30x+36-0.60x = 24
-0.30x+36 = 24
-0.30x+36-36 = 24-36 ... subtract 36 from both sides
-0.30x = -12
-0.30x/(-0.30) = -12/(-0.30) .... divide both sides by -0.30
x = 40
We need <font color=red size=4>40 liters</font> of the 30% solution


y = 60-x
y = 60-40
y = 20
and <font color=red size=4>20 liters</font> of the 60% solution


With those x and y values in mind, note that
30% of x = 30% of 40 = 0.30*40 = 12
60% of y = 60% of 20 = 0.60*20 = 12
Those values sum to 12+12 = 24, which was the amount of pure acid Gabe needs. 
This helps confirm we have the right answer.


---------------


Answers: 
<font color=red size=4>40 liters</font> of the 30% solution
<font color=red size=4>20 liters</font> of the 60% solution
</font>