SOLUTION: Mr Ronan had 2/3 as many yellow floorball sticks as red floorball sticks in the PE storeroom. He took 40 yellow floorball sticks and 18 red floorball sticks for a lesson. He then h

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Question 1206124: Mr Ronan had 2/3 as many yellow floorball sticks as red floorball sticks in the PE storeroom. He took 40 yellow floorball sticks and 18 red floorball sticks for a lesson. He then had 2/9 as many yellow floorball sticks left in the storeroom as red floorball sticks left. How many floorball sticks were there in the PE storeroom before the lesson?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Mr Ronan had 2/3 as many yellow floorball sticks as red floorball sticks in the PE storeroom.
He took 40 yellow floorball sticks and 18 red floorball sticks for a lesson.
He then had 2/9 as many yellow floorball sticks left in the storeroom as red floorball sticks left.
How many floorball sticks were there in the PE storeroom before the lesson?
~~~~~~~~~~~~~~~~~~~~~ 

Let x be the total number of the floorball sticks in the PE storeroom before the lesson,
and let y be the number of the yellow floorball sticks of them.


Then the number of red sticks in the storage room before the lesson was x-y.


From the given part, we have this proportion

    yellow = ,  or  y = .


Multiply both sides by 3 and simplify

    3y = 2(x-y),  --->  3y = 2x - 2y,  --->  3y + 2y = 2x,  --->  5y = 2x,  --->  y = .


    Thus the number of yellow sticks in the storeroom before the lesson was ,  or  0.4x.

         the number of red    sticks in the storeroom before the lesson was (x-0.4x) = 0.6x.


After taking 40 yellow floorball sticks and 18 red floorball sticks from the storeroom,
we have this equation

    0.4x-40 = .


Multiply both sides by 9, then simplify and find x

    9*(0.4x-40) = 2*(0.6x-18)

    3.6x - 360 = 1.2x - 36

    3.6x - 1.2x = 360 - 36

        2.4x    =   324

           x    =   324/2.4 = 135.


ANSWER.  The number of floorball sticks in the PE storeroom before the lesson was 135.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Given that the number of yellow was 2/3 the number of red....

let 2x = number of yellow
then 3x = number of red

After using 40 yellow and 18 red....
2x-40 = number of yellow left
3x-18 = number of red left

The number of yellow left was 2/9 the number of red:






The total number originally was 2x+3x = 5x = 5(27) = 135.

ANSWER: 135
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