SOLUTION: A lawn-care technician wants to spread a 200-lb seed mixture that is 50% bluegrass. If the technician has on hand a mixture that is 75% bluegrass and a mixture that is 10% bluegra

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Question 1205783: A lawn-care technician wants to spread a 200-lb seed mixture that is 50% bluegrass. If the technician
has on hand a mixture that is 75% bluegrass and a mixture that is 10% bluegrass, how many pounds of
each mixture are needed to make 200 lb of the 50% mixture? Round to the nearest whole pound.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A lawn-care technician wants to spread a 200-lb seed mixture
that is 50% bluegrass. If the technician has on hand a mixture
that is 75% bluegrass and a mixture that is 10% bluegrass, how
many pounds of each mixture are needed to make 200 lb of the
50% mixture? Round to the nearest whole pound.
                      lbs of      part     lbs of bluegrass
                      mixture   bluegrass    in mixture
stronger mixture         x         0.75         0.75x
weaker mixture           y         0.10         0.10y
final medium mixture    200        0.50         0.50(200)=100

The equations come from the first and last columns:

system%28x%2By=200%2C0.75x%2B0.10y=100%29

Simplify the second equation by clearing the decimals by multiplying
through by 100
system%28x%2By=200%2C75x%2B10y=10000%29

You can solve this simpler by elimination:

Multiply the first equation by -10 to make the y's cancel:

system%28-10x-10y=-2000%2C75x%2B10y=10000%29

Add the two equations term by term

65x = 8000
  x = 123.0769231 round to 123 of the stronger mixture

Since that's not easy to substitute, go back and
multiply the first equation by -75 to make the y's cancel:

system%28-75x-75y=-15000%2C75x%2B10y=10000%29

Add the two equations term by term

-65y = -5000
  y = 76.92307692 round to 77 pounds of the weaker.

As a partial mental check, think of the fact that it is logical
that you would use more of the stronger and less of the weaker, 
because 50% is closer to 75% than it is to 10%.  That's not a
perfect check, but if we had gotten less stronger than weaker, 
we would known such an answer would be wrong.

Edwin