Mixed model problem

Question

A 25% alchohol solution is to be mixed with a 45% water solution to obtain 8 liters of 35% alcohol solution. How many liters should be used?

Answer 1

Let x be the quantity of the 25% solution which is used and y the quantity of the 45% solution to be used.

 

Then x + y = 8 and .25x + .45y = .35(8). The first equation just states that the mixture totals 8 liters. The second equation states that the quantity of alcohol in each solution add together gives the amount of alcohol in the mixture.

 

You can start to solve this by clearing out the decimals and multiplying the second equation by 100:

 

   x +     y = 8

25x + 45y = 280.

 

You can then solve using substitution or elimination. I will use substitution on this one.

 

y = 8 - x  ⇒  25x + 45(8 - x) = 280

 

                   25x + 360 - 45x = 280

 

                   -20x = -80

 

                   x = 4.

 

Also, y = 8 - 4 = 4. The answer is that 4 liters of each solution were used.