Linear Equations

Question

a stained glass factory must have 18 liters of 20% acid solution for an etching bath, but has only 15% and 35% acid solutions available. How much of each 15% acid solution and 35% acid solution must be mixed to have the 18 liter of the 20% acid solution?

Answer 1

Hi Madison, to solve mixture problems, set up a table. Let x represent the amount of 15% solution. Then 18 - x will represent the amount of 35% solution needed.

 

Table:

 

Percent       Amount        Decimal           Total

----------------------------------------------------------

  15%             x                 .15          .15x

 

  35%         18 - x              .35         .35 * (18 - x)

 

  20%            18                .20         .20 * 18

 

Equation:

 

  .15x  + .35 * (18 - x) = .20 * 18

 

  .15x  + .35 * 18 - .35x = .20 * 18

 

  -.20x + 6.30 = 3.60

 

Add .20x to both sides:

 

  6.30 = .20x + 3.60

 

Divide both sides by 3.60:

 

  2.70 = .20x

 

Divide both sides by .20

 

  x = 13.5

 

The factory needs 13.5 liters of 15% acid solution.

 

The factory needs 18 - 13.5, or 4.5 liters of 35% acid solution.

 

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