SOLUTION: a manufacturer packages soap powder in containers of three different sizes the amount of soap powder in a full large container could fill exactly three of the medium containers or

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: a manufacturer packages soap powder in containers of three different sizes the amount of soap powder in a full large container could fill exactly three of the medium containers or       Log On


   

Question 1124967: a manufacturer packages soap powder in containers of three different sizes the amount of soap powder in a full large container could fill exactly three of the medium containers or exactly 5 of the smaller containers if an equal number of small and large containers are to be filled with the amount of soap powder that would fill 90 medium containers how many small containers would be filled ?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the capacity of a large container; then the capacity of a medium container is (1/3)x and the capacity of a small container is (1/5)x. So the ratio of the capacities of the three sizes of containers is

1 : 1/3 : 1/5

The problem could of course be worked that way; but I would prefer to express the ratio as whole numbers. Multiplied by the least common denominator 15, the ratio is

15 : 5 : 3

So now let the capacities of the three sizes of containers be
large: 15x
medium: 5x
small: 3x

The capacity of 90 medium containers will then be 90*5x = 450x.

The capacity of one large and one small container is 15x+3x = 18x.

The number of large and small containers required to have a capacity equal to 90 medium containers is

(450x)/(18x) = 25.

Answer: 25 small containers would have to be filled.