Big Book:Ratio Problem - A methodical way to solve this problem

[gre320hex]

Can we discuss a good way to solve this problem. I got this problem by solving it logically, but not sure if my mind would work that way during a test. I want to discuss a algebraic way to solve this problem.

Here is the question:

A manufacturer packages soap powder in containers of three different sizes. The amount of soap powder in a full large container could fill exactly 3 of the medium containers or exactly 5 of the small containers. If an equal number of small and large containers are to be filled with the amount of soap that would fill 90 medium containers, how many small containers will be filled?

A. 25
B 27
C. 30
D. 45
E. 54

[Mervin2008]

Can we discuss a good way to solve this problem. I got this problem by solving it logically, but not sure if my mind would work that way during a test. I want to discuss a algebraic way to solve this problem.

Here is the question:

A manufacturer packages soap powder in containers of three different sizes. The amount of soap powder in a full large container could fill exactly 3 of the medium containers or exactly 5 of the small containers. If an equal number of small and large containers are to be filled with the amount of soap that would fill 90 medium containers, how many small containers will be filled?

A. 25
B 27
C. 30
D. 45
E. 54

I got the answer as 54 ,is it correct ?If its correct I can explain the logic I am using

[gre320hex]

I got the answer as 54 ,is it correct ?If its correct I can explain the logic I am using

Sorry, here is the Official Answer .

SPOILER: A

.

Also, note that the question states "equal" number of small and large containers.

[mickgreen58]

1L = 3M
1L = 3S

90M = 30L or 150S

Let x be the number of containers each:
5x+x = 150 = 25

Im off to take the GRE, wish me luck

[gre320hex]

1L = 3M
1L = 3S

90M = 30L or 150S

Let x be the number of containers each:
5x+x = 150 = 25

Im off to take the GRE, wish me luck

Ok, all the best!

But, I am not sure how you came up with the equation 5x+x !!?

[hilldog]

3M = L = 5S

n(L+S) = 90M
n(5S+S) = 90*(5/3) S
so, n = 25.