Question 1086552
<font color="black" face="times" size="3">Let x = amount of the 90% acid solution (in centiliters)


We have 50 centiliters of the 40% solution. 
This means we have 0.4*50 = 20 centiliters of pure acid


We're adding on x more centiliters of the 90% solution. 
There are an additional 0.9*x centiliters of pure acid. 


In total, we have 0.9*x+20 centiliters of pure acid.


This is out of x+50 centiliters of solution. 


Divide the expressions 0.9*x + 20 over x+50 to get {{{(0.9*x + 20)/(x+50)}}}. 
This fraction represents the ratio of pure acid to total solution. 
We want this ratio to be equal to 50%. 
This is because we want the final solution to be 50% acid


So set {{{(0.9*x + 20)/(x+50)}}} equal to 0.50 to get {{{(0.9*x + 20)/(x+50) = 0.50}}}


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Now solve for x


{{{(0.9*x + 20)/(x+50) = 0.50}}}


{{{0.9x + 20 = 0.50(x+50)}}}


{{{0.9x + 20 = 0.50(x)+0.50*(50)}}}


{{{0.9x + 20 = 0.50x+25}}}


{{{0.9x + 20-0.50x = 0.50x+25-0.50x}}}


{{{0.4x + 20 = 25}}}


{{{0.4x + 20-20 = 25-20}}}


{{{0.4x = 5}}}


{{{(0.4x)/(0.4) = (5)/(0.4)}}}


{{{x = 12.5}}}


<font color=red>We need 12.5 (12 and a half) centiliters of the 90% solution. </font></font>