translate the given information into a system of equations.and write the conclusion. the question is below

Question

a chemist has three solutions of hydrochloric acid.one solution is 10% acid, the second is 20% acid, and the third is 40% acid. how many liters of each should mix to obtain 100 liters of a 25% acid solution?

Answer 1

Yes, indeed....we need 1 more piece of data.

 

X+Y+Z = 100 <--- 1st equation

 

0.1X +0.2Y + 0.4Z = 100*0.25 = 25

X+2y + 4z = 250  <--- 2nd equation

 

Let x be the free variable.

Then we have

 

y + z = 100 -x

 

2y + 4z = 250 - x

 

 

First equation shows:  z = 100 - x - y

Plugging that into the second equation :

 

2y + 4(100 -x - y) = 250 -x

2y + 400 - 4x - 4y = 250 -x

 

-2y + 400 - 4x = 250 -x

 

-2y = 250 -x - 400 + 4x

 

 -2y = -150 + 3x

 

y = 75 - (3/2)x

 

Then z = 100 -x - y = 100 - x - 75 + (3/2)x per hte equation above

 

           = 25 + (1/2)x

 

 

So in terms of x;

 

y = 75 - (3/2)x

 

 z = 25 + (1/2)x

 

 

Now, to keep things simple, let's restrict ourselves to WHOLE liters.

 

This works for x equal to any even positive integer less than 50,

so 2,4,6,8,...,44,46,48

 

So for example, if x=10 then

                          y = 60 and z = 30

 

10% of 10 + 20% of 60 + 40% of 30 =

 1 + 12 + 12 = 25

                    = 25% of 100

 

So there are 25 answers.

That;s what happens when all of the data is not given