NEED HELP WITH TABLES

Question

Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find the number of liters of 20% acid solution in the new mixture. Construct a table to organize the information, and show all of your work to solve the problem.

Answer 1

 

 

                                   Solution #1              Solution #2             Resulting Solution

 

    qty                               12 L                         ?                            12 + ?

 

  % acid                       8% = 0.08                20% = 0.2                    16% = 0.16

 

  qty acid                12 x 8% = 0.96L              0.2 x ?                       .16 x (12 + ?)

 

The equation is

 

0.96 + 0.2 x ? = 0.16 x ( 12 + ? )  <-- distributive 

 

Multiplies everything by 100 to clear the decimals:

 

96 + 20 x ? = 192 + 16 x ?

 

Moves everything to the left side:

 

96 + 20 x ? - 192 - 16 x ? = 0

 

Combines like terms:

 

4 x ? - 96 = 0

 

4 x ? = 96

 

? = 24

 

SO 24 L of the 20% acid solution is used.

 

 

CHECK: 0.08x12 + .2 x 24 = 5.76 L of acid

             5.76 / (12 +24) = 5.76/36 = 0.16 = 16% acid