SOLUTION: A chemist needs to mix a 75% saltwater soulution with a 50% saltwater solution to obtain 10 gallons of a 60% mixture. How much of each soultion is required?

Question 215275: A chemist needs to mix a 75% saltwater soulution with a 50% saltwater solution to obtain 10 gallons of a 60% mixture. How much of each soultion is required?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
A chemist needs to mix a 75% saltwater solution with a 50% saltwater solution to obtain 10 gallons of a 60% mixture. How much of each soltion is required?
0 solutions


We are mixing some stronger liquid (75%) with some 
weaker liquid (50%) to get a medium strength 
liquid (60%).

Make this chart:

                   Amount of  Percentage expressed    Amt. of
Solution            liquid        as a decimal       saltwater  
--------------------------------------------------------------
Stronger liquid     
Weaker liquid                   
Medium liquid                    

Fill in the percentages:

                   Amount of  Percentage expressed    Amt. of
Solution            liquid        as a decimal       saltwater  
--------------------------------------------------------------
Stronger liquid                      .75               
Weaker liquid                        .50             
Medium liquid                        .60              


There are to be 10 gallons of medium strength liquid.
Let x = the number of gallons of stronger liquid.
Then 10-x = the number of gallons of weaker liquid.

Fill those amounts in

                   Amount of  Percentage expressed    Amt. of
Solution            liquid        as a decimal       saltwater  
--------------------------------------------------------------
Stronger liquid        x             .75               
Weaker liquid        10-x            .50             
Medium liquid         10             .60              

Fill in the amount of saltwater by multiplying the amount of
liquid by the percentage:
 
                   Amount of  Percentage expressed    Amt. of
Solution            liquid        as a decimal       saltwater  
--------------------------------------------------------------
Stronger liquid        x             .75               .75
Weaker liquid        10-x            .50             .50(10-x)
Medium liquid         10             .60              .60(10)

Get the equation from

Amount of saltwater in stronger + Amount of saltwater in weaker = Amount of saltwater in final medium strength

.75x + .50(10-x) = .60(10) Solve that and get x=4 gallons of stronger strength liquid Then 10-x = 10-4 = 6 gallons of weaker strength liquid. Note as a partial check: Since the final medium strength liquid (60%) is more like the weaker strength liquid (50%) than it is like the stronger strength liquid (75%), we would expect there to be more of the weaker than the stronger. And that is what we ended up with, since 6 gallons is more than 4 gallons. Edwin

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