Fraction of Students Not Going on Trip with Given Junior and Senior Numbers

[zak100]

Homework Statement

1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip?

Homework Equations

Simple fraction based equations.

The Attempt at a Solution

Not Going to Trip = 1/4Juniors(J) + 2/3Seniors(S)I am not able to solve it completely because I can't understand what is meant by "2/3 as many juniors as seniors". I think that J=2/3S.

Some body please guide me.

Zulfi.

 

[Orodruin]

I think that J=2/3S.

This is correct. What fraction of all students are then juniors?

 

[zak100]

Hi,

What fraction of all students are then juniors?

It is not given in the question. I am not able to understand:
there are 2/3 as many juniors as seniors

Some body please guide me.

Zulfi.

 

[Ray Vickson]

Hi,It is not given in the question. I am not able to understand:
there are 2/3 as many juniors as seniors

Some body please guide me.

Zulfi.

You have already been told that your expression $J = (2/3)S$ is correct.

 

[zak100]

Hi,
Trip= 1/J + 2/3*3/2J
Trip= 5J/4
Now we have three unknowns and two equations. How can we solve it? Should we suppose value.

Zulfi.

 

[Orodruin]

Hi,It is not given in the question. I am not able to understand:
there are 2/3 as many juniors as seniors

Some body please guide me.

Zulfi.

You are missing a crucial assumption that is subtextual. How large a fraction of the total students are juniors or seniors?

 

[zak100]

Hi,
I have not considered students not going to trip but it would create one more unknown. How to solve this problem.

Zulf.

 

[Orodruin]

How to solve this problem.

By thinking about the hints you are given and using them instead of ignoring them. You have still to answer the question posed in both post #2 and #6.

 

[zak100]

Hi,
Post#2 answer= 5j/4 (as shown in post#5)
Post#6 answer=I don't know. (You are asking for large. However Question is not asking any large value. It is asking what fraction of students did not go for the trip.)
Kindly tell me if my post#2 answer is correct or not??

Zulfi.

 

[Mark44]

From post #2:

What fraction of all students are then juniors?

Post#2 answer= 5j/4 (as shown in post#5)

No, this isn't possible. The number of juniors can't be 5/4 of the number of juniors.

The question does not ask for the total numbers of juniors and seniors. Further, there isn't enough information given to be able to determine these numbers. However, there is enough information to answer the question.

I'll try to help you get started in a more organized way.
Let J = the number of juniors
Let S = the number of seniors

• The number of juniors and seniors is J + S
• The number of juniors and seniors going on the trip is $\frac J 4 + \frac{2S} 3$ -- you have this in post #1
• It's given that there are 2/3 as many juniors as seniors, so $J = \frac 2 3 S$ -- you also have this in post #1

Now, what expression represents the total number of juniors and seniors NOT going on the trip?

Once you have that, you can write a fraction that represents the fraction of juniors and seniors not going on the trip.

 

[zak100]

Hi,
I found that deriving equation is really a difficult for me. So i have switched to using values. This is what GRE is also doing. However, i did not look at their solution but my answer is correct.

JTrip = 1/4J
STrip = 2/3S
Now its given J= (2/3)S
At this point its clear that Senior S is greater than Junior J. So let's chose 90 as the value for S.
J=(2/3 ) 90 = 60
Now JTrip = (1/4) * 60 = 15
STrip = (2/3) * 90 = 60
Total on Trip = 60 +15 = 75
Total in School = 90 + 60 = 150
Total not in Trip = 150-75=75
Fraction = 75/150 = 1/2

Zulfi.