You need 455 ml of a 75% alcohol solution. on hand, you have a 25% alcohol mixture. you also have a 90% alcohol mixture. how much of each mixture will you need to add to obtain the desired solution?

X ml - 25% alcohol mixture
y ml - 90% alcohol mixture

x+y = 455 

0.25x ml alcohol in x ml of  25% alcohol mixture
0.9y ml alcohol in y ml of  90% alcohol mixture
0.75*455= 341.25 ml alcohol in 455 ml of  75% alcohol mixture

0.25x+0.9y=341.25 

System of equations:

x+y = 455 /*(-0.25) > -0.25x-0.25y = -0.25*455 
0.25x+0.9y=341.25

-0.25x-0.25y=-113.75
0.25x+0.9y=341.25    Add both equations

0.25x+0.9y-0.25x-0.25y=341.25-113.75
0.65y =227.5
y=227.5/0.65 = 350 ml  of  90% alcohol mixture

x+y=455
x+355=455
x=100 ml of  25% alcohol mixture