Question 1040489: In an art class,  of the students are girls and  of girls are seniors. If  of senior girls have passed the final art test, which of the following could be the number of students in this class?.
A) 20
B) 30
C) 45
D) 60
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you need to test each one out to see which ones are possible.
if the total is 20, and 2/3 are girls, then the number of girls is 20 * 2/3 = 13 and 1/3 which is not possible, so it can't be 20.
if the total is 30, and 2/3 are girls, then the number of girls is 20 which is possible.
if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 20 = 40/5 = 8 which is possible.
if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 8 = 8/3 which is equal to 2 and 2/3 which is not possible, so it can't be 30.
if the total is 45, and 2/3 are girls, then the number of girls is 30 which is possible.
if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 30 = 12 which is possible.
if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 12 = 4 which is possible, so a total of 45 is possible.
if the total is 60, and 2/3 are girls, then the number of girls is 40 which is possible.
if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 40 = 16 which is possible.
if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 16 = 5 and 1/3 which is not possible.
the only possible number of students is therefore 45.
you could also have done this algebraically as follows:
let g = number of girls.
let t = total number of students.
2/3 of the students are girls.
you get g = 2/3 * t.
2/5 of the girls are seniors.
let s = number of seniors.
you get 2/5 * g = s
since g = 2/3 * t, you get 2/5 * 2/3 * t = s
simplify to get 4/15 * t = s
let p = number of senior girls who passed the final
you get p = 1/3 * s
since s = 4/15 * t, you get 1/3 * 4/15 * t = p
simplify to get 4/45 * t = p
you can use this last formula to determine what the number of t could be.
if t = 20, then 4/45 * 20 = p which results in p = 1.78 which is not possible.
if t = 30, then 4/45 * 30 = p which result in p = 2.67 which is not possible.
if t = 45, then 4/45 * 45 = 4 which is possible *****
if t = 60, then 4/45 * 60 = 5.33 which is not possible.
the only possible situation that results in p being equal to an integer is when the total number of student = 45, so that has to be your solution.
|
|
|
