SOLUTION: A horticulturist wants to mix three types of fertilizers, which contain 20%, 30%, 40% nitrogen, respectively. If the final mixture should be 1000 pounds of 32% nitrogen , all three

Question 336568: A horticulturist wants to mix three types of fertilizers, which contain 20%, 30%, 40% nitrogen, respectively. If the final mixture should be 1000 pounds of 32% nitrogen , all three types are used, and there is twice as much of the 40% type as of the 20% type, how much is in the final mixture.
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
A horticulturist wants to mix three types of fertilizers, which contain 20%, 30%, 40% nitrogen, respectively. If the final mixture should be 1000 pounds of 32% nitrogen , all three types are used, and there is twice as much of the 40% type as of the 20% type, how much is in the final mixture.
let the mass of 20,30,40 be m2,m3,m4, then
1) m2+m3+m4=1000
2) 0.2*m2+0.3*m3+0.4*m4=.32*1000
3) m4=2*m2
3=>) m2+m3+2*m2=1000
0.2*m2+0.3*m3+0.4*2*m2=320
3*m2+m3=1000 => m3=1000-3*m2
0.2*m2+0.3*1000-0.9*m2+0.8*m2=320
0.1*m2=320-300=20
m2=200 pounds
m3=1000-3*200=400 pounds
m4=400 pounds
(Verif : 200+400+400=1000 pounds
400=2*200
and .2*20+.4*30+.4*40=4+12+16=32 %
)
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