Systems of Linear Equations

Question

a birding club holds an annual photography contest. After a set time limit in a park, contestants receive 4 points for photos of songbirds and 20 points for photos of birds of prey. Last year's winner had a total of 200 points from 38 photos of individual birds. How many of each type of bird did the winner photograph?

Answer 1

Let x = number of songbird photos

       y = number of birds of prey photos

 

Then,    x +      y = 38

   and   4x + 20y = 200

 

Divide the second equation by 4.  

 

So, we have x + y = 38

                      x + 5y = 50

 

Subtracting the equations, we get -4y = -12

                                                                y = 3 and x + 3 = 38

                                                                                     So, x = 35

 

The winner took 35 songbird photos and 3 photos of birds of prey.