How much of each chemical is needed to make 750 kg of the plant food, if a plant food is to be made from three chemicals and the mix must include 60% of the first and second chemicals, the second and third chemicals must be in a ratio of 4 to 3 by weight?

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Answer 1 · 2015-03-31T03:46:51

1st chemical 50 kg, 2nd chemical 400 kg, 3rd chemical 300 kg

Let #a#, #b#, #c# be the weights of three chemicals, then as per the question

#a+b+c= 750# and

#a+b= 60% "of 750" = 750*60/100 = 450#

Clearly #c# will be #750-450 = "300 kg"#

Now ratio of #b# to #c# is #4:3#, that means

#b/c= 4/3 <=> 3b = 4c#

Since #c# is #"300 kg"#, as calculated above,

#3b= 3(400)= 1200#

Hence #b =400#. Now, since

#a+b =450 implies a= 450-400 = "50 kg"#

Thus chemicals #a#, #b#, and #c# in #"750 kg"# of plant food would be #"50 kg"#, #"400 kg"#, and #"300 kg"#.