word problems and turning them into algebraic equation to slove

Question

How many liters of a 35% acid solution should be mixed with 5 liters of a 25% acid solution to produce a 34% solution?

 

Put into an algebraic equation for solving

Answer 1

In order to put this problem into an algebraic equation it can be written as 5L*(.25) + XL*(.35) = (X+5)*(.34)

 

The reason we multiply 5 by .25 is to get the percentage of acid that is present in the solution.

 

X * .35 represents the X amount of acid that is in the 35% solution.

 

In order to find the total amount of acid in the solution we have to add them both together. 

 

Since it is the total amount of acid in solution we have to remember that not just acid is being added, solution is also being added. That is why on the right, (X + 5) is written. 

 

(X+5) represents the total amount of solution (acid included).

 

Finally we multiply the (X+5) because we want to reach a solution of 34% acid.

 

So just solve for X.

 

5(.25)+X(.35)=(X+5).34

 

x(.35) = X(.34) + 5(.34) - 5(.25)

 

X(.35) - X(.34) = 5(.34) - 5(.25)

 

X(.35 - .34) = 5(.34 - .25)

 

X(.01) = 5(.09)

 

X = 45 liters

Answer 2

"How many liters of a 35% acid solution should be mixed with 5 liters of a 25% acid solution to produce a 34% solution?"

We have 5 liters of 25% acid solution. which mean it has 0.25 * 5 = 1.25 liters of pure acid mixed with water. 

We will add "x" liters of 35% acid solution to make a 34% solution.

So, at the conclusion, we will have (5 + x) * 34% liters of pure acid.

That can be shown with the equation:  

0.25*5 + 0.35x = 0. 34(5 + x)

1.25 + 0.35x = 1.7 + 0.34x

0.34x - 0.34x = 1.7 - 1.25

0.01x = 0.45

x =  0.45 / 0.01 

x = 45 liters