word problems mixing potash and fertilizers

Question

 A hortucurtualiast  needs a fertilizer that is 8% potash, but she can only find fertilizers that contain 6% and 15% potash. How much of each should she mix to obtain 10 pounds of fertilizer that is 8% potash?

Answer 1

 

 

10 lbs of potash at 8% = .08 x 10 = .8 lbs.

 

We need .8 lbs of potash.

 

Let x be the # of lbs of 6%.

10 - x would be the # of lbs of the 15%, since we can only have 10 lbs at the end.

 

x(.06) + (10-x)(.15) = .8 lbs

 

.06x + 1.5 - .15x = .8

 

1.5 - .09x = .8

 

-.09x = .8 - 1.5

 

-.09x = -.7

------     ----

-.09       -.09

 

x = 7.78 lbs of 6%

 

10 - x = 10 - 7.78  = 2.22 lbs of 15%.

 

 

Double check:

(7.78 lbs)(.06) + (2.22 lbs)(.15) = 

.467 lbs potash = .333 lbs potash = .8 lbs potash in 10 lbs of the mixture.