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:
Simplify the second equation by clearing the decimals by multiplying
through by 100
You can solve this simpler by elimination:
Multiply the first equation by -10 to make the y's cancel:
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:
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