there were several great blue herons and roseate spoonbills

Question

Exact questionthere were several great blue herons and roseate spoonbills right outside jim's vacation home. jim realizes that if 6 roseate spoonbills fly away only 1/7 of the remaining birds will be roseate spoonbills, and if 4 great blue herons fly away(and no roseate fly away) 1/2 of the remaining birds will be great blue herons. How many birds are outside ji's home?

Answer 1

Total number of birds = x

 

number of roseate spoonbills = 6 + x/7

 

number of  blue herons =  4 +x/2

 

now we can write equation as

 

6+x/7 + 4+x/2 = x

 

10 + x/7 +x/2 = x

 

LCM of denominator is 14

 

140 + 2x +7x = 14x

 

140 = 5x

 

28 = x

 

total number of birds = 28