Question

Steve saw 313 birds during a bird-watching trip to Yellowstone National Park. He observed 15 more trumpeter swans than sand-hill cranes. He saw twice as many mountain chickadees as dusky grouses. How many birds of each type did Steve observe if he saw half as many trumpeter swans as dusky grouses?

Answer 1

trumpeter swans = t = 41

sand-hill cranes = s = 26

chickadees = c = 164

dusky grouses = d = 82

Explanation:

Total birds = 313

Let

trumpeter swans = t

sand-hill cranes = s

chickadees = c

dusky grouses = d

t = 15 + s

c = 2d

d = 2t

t + s + c + d = 313

(15+s) + s + 2d + d = 313

15 + s + s + 2(2t) + 2t = 313

15 + 2s + 4t + 2(15+s) = 313

15 + 2s + 4(15 + s) + 30 + 2s = 313

15 + 2s + 60 + 4s + 30 + 2s = 313

105 + 8s = 313

8s = 313 - 105

8s = 208

s = 208 / 8

= 26

s = 26

t = 15 + s

= 15 + 26

= 41

d = 2t

d = 2(41)

= 82

c = 2d

c = 2(82)

= 164

trumpeter swans = t = 41

sand-hill cranes = s = 26

chickadees = c = 164

dusky grouses = d = 82