Problem Solving question

[parallel_chase]

45% of the students in a school are girls. Among the students who have traveled abroad earlier, 25% are girls, and among the ones who have not, 25% are boys. If the difference between the number of students who have traveled outside the country and the number of those who have not is 105, what is the total number of students in that school?

A. 852
B. 754
C. 620
D. 525
E. 458


I keep getting the 2100 as the answer. Any help and explanation is much appreciated.

Thanks,
Adi

[szapiszapo]

the answer is D, i.e. 525

Your answer is 4 times bigger. I believe that you got rid of the % somewhere in the process, taking numerical values of 25 and 75 instead of 1/4 and 3/4.

[parallel_chase]

the answer is D, i.e. 525

Your answer is 4 times bigger. I believe that you got rid of the % somewhere in the process, taking numerical values of 25 and 75 instead of 1/4 and 3/4.

Thank you for replying. The answer is indeed 525. But i am still getting 2100 as the answer. Below is my working, hopefully you will be able spot the mistake.

x be the total number of students

therefore, 45% of x = total number of girls (G)
55% of x = total number of boys (B)

students traveled abroad

25%G + 75%B

students not traveled abroad

75%G + 25%B

Therefore,

25%G + 75%B - 75%G - 25%B = 105

B - G = 210

substituting the values of B and G here

55%x - 45%x =210

x = 2100

Thanks

[szapiszapo]

Thank you for replying. The answer is indeed 525. But i am still getting 2100 as the answer. Below is my working, hopefully you will be able spot the mistake.

x be the total number of students

therefore, 45% of x = total number of girls (G)
55% of x = total number of boys (B)

students traveled abroad

25%G + 75%B

students not traveled abroad

75%G + 25%B

Therefore,

25%G + 75%B - 75%G - 25%B = 105

B - G = 210

substituting the values of B and G here

55%x - 45%x =210

x = 2100

Thanks

it seems to me that you are assuming that 25% of all school girls have travelled abroad before, whereas the wording says that school girls that travelled abroad before represents 25% of the number of kids that went abroad. which is different, as in fact the number of kids that went abroad is 1,5x higher than the number of kids that didnt.

you are making the same mistake for boys.
i believe it comes from there.

[asigheartau]

Adi,

let x total no. of students
y= students gone abroad
z= students NOT gone abroad

45%x= Girls
55%x Boys

Next, we find out that 25% of the students gone abroad are girls, therefore:
25%Y= Girls=>75%Y= Boys

For students not gone abroad:

25%Z=Boys and 75%Z=Girls

From the beginning we know that
X( Total no. of students) = Y(students gone abroad)+Z(Not gone abroad)

expressing it in terms of x as two equations gives:

45%x-25%Y=75%Z
55%x-75%y=25%Z => z=2x/5 & y=3x/5

We also know that the difference between students who went abroad and students who did not: 105

Therefore: y-z=105=> 3x/5-2x/5=105
x/5 = 105 so x is 525

I hope it helped.
mult succes in continuare

[dbart06]

asigheartau,

could you elaborate onn how you got:

45%x-25%Y=75%Z
55%x-75%y=25%Z => z=2x/5 & y=3x/5

thanks

[parallel_chase]

asigheartau,

could you elaborate onn how you got:

45%x-25%Y=75%Z
55%x-75%y=25%Z => z=2x/5 & y=3x/5

thanks

Since X = Y + Z

therefore,

for Girls

45%X = 25%Y + 75%Z => 45%X - 25%Y= 75% Z

similarly for boys,

55%X = 75%Y + 25%Z => 55%X - 75%= 25%Z

if you solve these equations you will get

Z = 2X/5
Y = 3X/5

I hope this helps.

Thanks a lot asigheartau for all the help. I wish there could be an easier way to solve this question. This method also works fine but it is a little time consuming.

[dbart06]

My brain may be fried from studying so much but I don't see what process ya'll are doing to come to the conclusion.

[dbart06]

My brain may be fried from studying so much but I don't see what process ya'll are doing to come to the conclusion.

[parallel_chase]

My brain may be fried from studying so much but I don't see what process ya'll are doing to come to the conclusion.

Dont worry it happens to best of us at worst of times. Just relax.

Now, let me know where are you facing the problem. Understanding the equations or solving the equation.

If you are having problems understanding the equation then let me know till what point were you able to understand the explanation given by asigheartau.

[dbart06]

I am not following how the formulas:

45%x-25%y=75%z
55%x-75%y=25%z

equates to z=2x/5 and y=3x/5

I understand everything before and after this point.

Thanks for helping.

[dbart06]

I am not following how the formulas:

45%x-25%y=75%z
55%x-75%y=25%z

equates to z=2x/5 and y=3x/5

I understand everything before and after this point.

Thanks for helping.

[parallel_chase]

I am not following how the formulas:

45%x-25%y=75%z
55%x-75%y=25%z

equates to z=2x/5 and y=3x/5

I understand everything before and after this point.

Thanks for helping.

To solve the above given equations you have to eliminate one variable.

If you need the value of Z in terms of X you have to eliminate Y, similarly if you need the value of Y in terms of X you have to eliminate Z.


If we multiply entire equation 45%x-25%y=75%z by 3
=> 135%x - 75%y = 225%z

Now look at the other equation 55%x-75%y=25%z

Subtract the two equations

135%x - 75%y=225%z
(-) 55%x - 75%y = 25%z
_____________________
80%x - 0 = 200%z

80x/200 = z

2x/5 = z


Similarly you multiply the second equation with 3 and eliminate Z to find out the value of Y in terms of X.

Hope this helps, if you still have any questions let me know. Try solving the second equation with the same method you will be able to find the answer.

[dbart06]

man, studying so much can make the simplist things seem difficult. I thought you would subtract the 2 equations but had a brain lapse and couldn't fiqure out how. Thanks a bunch....I can breathe easier now.

[parallel_chase]

man, studying so much can make the simplist things seem difficult. I thought you would subtract the 2 equations but had a brain lapse and couldn't fiqure out how. Thanks a bunch....I can breathe easier now.

no worrys, like I said before it happens to best of us at worst of times.

Good luck.