Question

In a study of bat migration habits, 240 male bats and 160 female bats have been tagged. If 100 more female bats are tagged, how many more male bats must be tagged so that 3/5 of the total number of bats in the study are male? Plz explain

Answer 1

Remark 
The way you have to set this up is to take the new number for the males and put it over the total for the males and females. The new number for the males / total = 3/5.

Step One
Find the total number of females
100 + 160 = 260 when 100 females have been added to the study.

Step Two 
Find the number of males
The total number of males = 240 + x where x is the number of males to be added.

Step Three
Find the total for both
260 + 240 + x = Total
500 + x = Total.

Step Four
Find the ratio of males to total
(240 + x) / (500 + x) = 3/5   

Step Five
Cross multiply and solve
(240 + x)*5 = (500+x)*3
1200 + 5x = 1500 + 3x    Subtract 1200 from both sides.
5x = 1500 - 1200 + 3x     
5x = 300 + 3x                   Subtract 3x from both sides.
5x - 3x = 300
2x = 300                          Divide by 2 
x = 300  / 2
x = 150

Check
(240 + 150 ) / (500 + 150) = ? 3/5
390 / 650 = ? 3/5
39/65 = ? 3/5  Divide the top and bottom on the left by 13
3/5 = 3/5 and it checks. 

Answer 2

Given:
Original ratio of tagged male : female = 240:160
Final proportion of tagged male = 3/5
Increase in number of females = 100
Need increase in number of males to maintain the required proportion.

Original ratio
male:female
= 240 : 160    [ GCF of 240 and 160 is 80, so divide by GCF ]
= 3 : 2   

Proportion of male/population
= 3/(3+2)
=3/5   so proportion will not change

Final number of females 
= 160+100
= 260

Final number of males
= 260*(final ration of male : female)
=260*(3/2)
= 390

Increase in number of males
= final - initial
= 390 - 240
= 150

Check: 
final proportion of male/population
= 390 / (390+260)  
= 390 / (650)        [ GCF of 390 and 260 = 130 , simplify fraction ]
= 3 / 5  ................. as required, ✔