Marie mixes 16 liters of 78% acid solution with a 25% acid solution to make a 41% acid solution. how many liters of 25% solution did she use

Let x be the number of liters of 25/% solution, then the number of liters of  41% solution will be x + 16  liters.

so we have 0.25x + 16* 0.78 = 0.41(x + 16)

solve this equation for x

   

16 liters of 78% acid solution.

let there be x of 25% acid solution.

The solution resulted in 41% acid solution, total volume = (x + 16) liters.

Using formula for mixture:

p1*v1 + p2*v2 = pv

where p1 is the % for the 1st and  v1 = volume of the first.

p2 is the % for the second and  v2 = volume of the second.

p is the final % and  v1 = total volume.

78%*16 + 25%*x  =  41%*(16+x)

Cancel out the % on each side.

78*16 + 25x = 41*(16 + x)

1248 + 25x  = 41*16 + 41*x

25x - 41*x = 41*16 - 1248

25x - 41x = 656 - 1248

-16x = -592

x = -592/-16

x ≈ 37

So Marie used 37 liters of the 25%.

Hope this helps.