Question

steve saw 313 birds during a bird-watching trip to Yellowstone National park. he observes 15 more trumpeter swans than sandhill cranes. he saw twice as many mountain chickadees as ducky grouses. how many birds of each type did steve observe if he saw half as many trumpeter swans as ducky grouses

Answer 1

• trumpeter swans = 41
• sandhill cranes = 26
• mountain chickadees = 164
• ducky grouses = 82

Explanation:

Total number of birds = 313

• trumpeter swans = s
• sandhill cranes = c
• mountain chickadees = m
• ducky grouses = g

We have equations below based on given:

s = c + 15

• m = 2g ⇒ m = 2(2s) = 4s ⇒ m = 4(c + 15)
• g = 2s ⇒ g = 2(c + 15)
• s + c + m + g = 313

Substituting m, g and s as above in the last equation and finding the value of c:

• c + 15 + c + 2(c + 15) + 4(c + 15) = 313
• 7(c + 15) + c = 313
• 7c + c + 105 = 313
• 8c = 313 - 105
• 8c = 208
• c = 208/8
• c = 26

Then finding the other values:

• s = 26 + 15 = 41
• g = 2s = 2*41 = 82
• m = 2g = 2*82 = 164