SOLUTION: Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 19,820 units of the first nutrient

Question 1144315: Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 19,820 units of the first nutrient and 32,090 units of the second nutrient. Each bacterium of species A requires 4 units of the first nutrient and 5 units of the second, and each bacterium of species B requires 1 unit of the first nutrient and 6 units of the second. What populations of each species can coexist in the environment so that all the nutrients are consumed each day?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

Let x be the number of species A  and y be the number of species B.


The most difficult part of the solution is to setup the equations.


From the condition, you have these two equation


    4x + 1y = 19820  units of the first nutrient     (1)

    5x + 6y = 32090  units of the second nutrient    (2)


These equations -- this system of equations -- is your setup.


At this point, the setup is just completed.


Now you should solve it.

You can use different methods: Substitution, Elimination, using determinants (the Cramer's rule).


For example, you may express  y = 19820-4x from the first equation and then substitute it into the second


    5x + 6*(19820-4x) = 32090.


It gives you  x =  = 4570.

Then  y = 19820 - 4*4570 = 1540.


ANSWER.  4570 species of the type A  and  1540 species of the type B.

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If you want to see other similar solved problems, look into the lesson
    - Roses and vilolets
    - Counting calories and grams of fat in combined food
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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