Question 107937
AT LEAST YOU GAVE IT A SHOT BUT YOU ARE GENERALLY FAR BETTER OFF IF YOU LAY OUT THE WORD PROBLEMS (WHAT EQUALS WHAT) AS I HAVE DONE BELOW.

Let x=the amount of 95% alcohol mixture
Then 10-x=amount of 15% alcohol mixture

Now we know that the amount of pure alcohol in the 95% mixture (0.95x) plus the amount of pure alcohol in the 15% mixture (0.15(10-x)) has to equal the amount of pure alcohol in the 45% mixture (0.45*10).  So our equation to solve is:

0.95x+0.15(10-x)=0.45*10 get rid of parens (distributive law)
0.95x+1.5-0.15x=4.5   subtract 1.5 from both sides

0.95x+1.5-1.5-0.15x=4.5-1.5  collect like terms

0.80x=3  divide both sides by 0.80

x=3.75 liters-----------amount of 95% alcohol mixture
10-x=10-3.75= 6.25 liters-----------------amount of 15% alcohol mixture

CK
0.95*3.75+0.15*6.25=0.45*10
3.5625+0.9375=4.5

4.5=4.5

ANOTHER WAY

Let x=amount of 95% alcohol mixture
And let y=amount of 15% alcohol mixture
Now we are told that:

x+y=10----------------------eq1
We also know that:

0.95x+0.15y=0.45*10------------------eq2

From eq1, y=10-x.  Substitute this into eq2 and we get:

0.95x+0.15(10-x)=4.5-----------------same equation as before.


Hope this helps---ptaylor