How much of the 85% mixture will you need to add to obtain the desired solution?

Question

You need a 80% alcohol solution. On hand, you have a 50 mL of a 25% alcohol mixture. You also have 85% alcohol mixture.

Answer 1

Hi Jennifer, to solve mixture problems, create a table to represent the data.

 

Let x be the amount of 85% solution needed.

 

Solution        Amount          Decimal          Total

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

25%               50ml               .25          .25 * 50

 

85%                 x                   .85          .85 * x

 

80%              50 + x              .80          .80 * (50 + x)

 

The total of the 25% solution plus the total of the 85% solution must equal the total of the 80% solution.

 

.25 * 50 + .85 * x = .80 * (50 + x)

 

Multiply by 100 to clear decimals:

 

25 * 50 + 85x = 80 * (50 + x)

 

Clear parenthesis:

 

1250 + 85x = 4000 + 80x

 

Subtract 80x from both sides:

 

1250 + 5x = 4000

 

Subtract 1250 from both sides:

 

5x = 4000 - 1250

 

5x = 2750

 

Divide both sides by 5:

 

x = 550

 

You need 550 ml of the 85% solution added to the 50 ml of 25% solution to get the necessary 80% solution.

 

Questions?