SOLUTION: Sparrows and pigeons sit on a fence. When 5 sparrows leave, there remain 2pigeons for every sparrow. Then 25 pigeons leave and the ratio of sparrows to pigeons becomes 3 : 1.What i

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Sparrows and pigeons sit on a fence. When 5 sparrows leave, there remain 2pigeons for every sparrow. Then 25 pigeons leave and the ratio of sparrows to pigeons becomes 3 : 1.What i      Log On


   

Question 285772: Sparrows and pigeons sit on a fence. When 5 sparrows leave, there remain 2pigeons for every sparrow. Then 25 pigeons leave and the ratio of sparrows to pigeons becomes 3 : 1.What is the original number of birds?
A. 50 B. 48 C. 75 D. 30 E. None of these.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Sparrows and pigeons sit on a fence.
When 5 sparrows leave, there remain 2pigeons for every sparrow.

What is the original number of birds?
:
"When 5 sparrows leave, there remain 2pigeons for every sparrow.
%28s-5%29%2Fp = 1%2F2
Cross Multiply
p = 2(s-5)
p = 2s - 10
:
"Then 25 pigeons leave and the ratio of sparrows to pigeons becomes 3 : 1.
%28s-5%29%2F%28p-25%29 = 3%2F1
Cross multiply
s-5 = 3(p-25)
s - 5 = 3p - 75
s = 3p - 75 + 5
s = 3p - 70
:
Replace p with (2s-10) derived from the 1st ratio
s = 3(2s-10) - 70
s = 6s - 30 - 70
s = 6s - 100
100 = 6s - s
s = 100%2F5
s = 20 sparrows
then
p = 2(20) - 10
p = 30 pigeons
:
A total of 50 birds
:
You can check the solutions in the two ratio statements