mixture of oats that is 12 percent, using 16 percent and 10 percent. need to make 27 lbs. 12 perecent of mixture

Question

heidi needs to make a mixture of oats that is 12 percent, using 16 percent and 10 percent how much of each does she need to make 27 lbs. 12 perecent mixture

Answer 1

Hi Kim, the best way to solve mixture problems is to create a table. Here is one solution:

 

Let x represent the pounds of 10% mixture

 

Then 27 - x is the amount of 16% mixture she needs

 

Percent     Pounds     Decimal    Total

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

10%             x             .10         .10x

 

16%         27 - x          .16       .16(27 - x)

 

12%            27            .12       .12(27)

 

Solution:

 

The pounds of 10% mixture plus the pounds of 16% mixture must equal the pounds of 12% mixture.

 

.10x + .16(27 - x) = .12(27)

 

I do not like to work with decimals, so multiply the entire equation by 100:

 

10x + 16(27 - x) = 12(27)

 

Clear parenthesis:

 

10x + 432 - 16x = 324

 

Combine terms on both sides:

 

6x = 108

 

Divide both sides by 6:

 

x = 18

 

Heidi needs 18 pounds of the 10% mixture.

 

Heidi needs 27 - 18, or 9 pounds of the 16% mixture.

 

Questions?