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.
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, ✔
