Algebra two word problem

Question

The cornelsen zoo has now added an aviary section with three different types of birds.The total number of kiwis,loons, and mocking birds is 73.Twice the number of kiwis is eleven less than the sum of loons and three times the mockingbirds.Two more than six times the number of mockingbird is the same as the sum of the kiwis and three times the loons.Write out each equation and state how many there are of each type of bird?

Answer 1

Sounds like a system of 3 equations with 3 unknowns

 

K + L + M = 73

 

2K = L + 3M - 11

 

6M + 2 = K + 3L

 

 

K + L + M = 73     EQ1

2K - L - 3M = -11  EQ 2

-K  -3L + 6M = -2  EQ 3

 

 

Let's reduce this to two variables by eliminating L   

Add EQ1 with EQ2

 

3K - 2M = 62    EQ4

 

 

Now triple EQ1 and add to EQ3

 

2K + 9M = 217    EQ5

 

 

 

So now we have 2 unknowns

 

3K - 2M = 62   EQ4

2K + 9M = 217    EQ5

 

Double EQ4 and Triple EQ5 and subtract

 

31M = 527

 

divide by 31, M = 17

 

sub M = 17 back into EQ 4

 

3K -34 = 62

 

3K = 96

 

K = 32

 

NOW sub M = 17 and K = 32 back into EQ1

 

32 + L + 17 = 73

 

49 + L = 73

 

L = 24