SOLUTION: Chairs are arranged in the hall into 18 short rows and 7 long rows. Each long row has 18 more chairs than each short row. 1/2 of the chairs are arranged into long rows. 3/7 of the

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Question 1205847: Chairs are arranged in the hall into 18 short rows and 7 long rows. Each long row has 18 more chairs than each short row. 1/2 of the chairs are arranged into long rows. 3/7 of the chairs are arranged into short rows. The remaining chairs are stacked in a corner.
(a) What fraction of the chairs are stacked in the corner?
(b) How many chairs are arranged in long rows?
Found 4 solutions by josgarithmetic, greenestamps, ikleyn, Edwin McCravy:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


1/2 of the chairs are arranged in long rows; 3/7 of them are arranged in short rows. The remainder are stacked in a corner.

1/2 + 3/7 = 7/14 + 6/14 = 13/14

(a) ANSWER: 1 - 13/14 = 1/14 of the chairs are stacked in the corner.

Using the fractions 7/14 and 6/14 from the preceding calculation....

let 7x = number of chairs in the 7 long rows
let 6x = number of chairs in the 18 short rows

Then the number of chairs in each long row is 7x/7 = x
And the number of chairs in each short row is 6x/18 = x/3

The number of chairs in each long row is 18 more than the number in each short row:

x - (x/3) = 18
(2/3)x = 18
x = 18(3/2) = 27

(b) ANSWER: the number of chairs in long rows is 7x = 7*27 = 189
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
Chairs are arranged in the hall into 18 short rows and 7 long rows.
Each long row has 18 more chairs than each short row.
1/2 of the chairs are arranged into long rows.
3/7 of the chairs are arranged into short rows.
The remaining chairs are stacked in a corner.
(a) What fraction of the chairs are stacked in the corner?
(b) How many chairs are arranged in long rows?
~~~~~~~~~~~~~~~~~~~~~~~~


        I use different setup comparing with that of @greenestamps. 


(a)  The answer for question (a) is simple arithmetic

         1 -  -  = write with common denominator of 14 = 1 -  -  = 1 -  = .

     We will use this value 1/14 in part (b).



(b)  Part (b) is more interesting. Its setup is quite unusual.


     Let x be the number of chairs in each long row.

     Then the number of rows in short rows is (x-18), according to the problem.


     The number of rows in all 7 long rows is 7x.

     The number of chairs in all 18 short rows is 18*(x-18).


     Since 1/2 of the chairs are arranged into long rows, the total number of chairs is twice 7x, or 14x.
     Hence, the other half is 7x, and it consists of 18*(x-18) chairs in short rows AND 1/14 of the total chairs, 14x, in the corner.


     Based on it, we can write this equation for the second half

         7x = 18*(x-18) + .


     The setup is complete. Now simplify the last equation and find x

         7x = 18x - 324 + x

         324 = 18 + x - 7x

         324 = 12x

           x = 324/12 = 27.


     Thus we get for (b) 27 chairs in each long row and 27*7 = 189 chairs in all 7 long chairs, altogether.

Solved.



Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
x = no. of chairs in a short row.
18x = no. of chairs in all 18 short rows
x+18 = no. of chairs in each long row.
7(x+18) = 7x+126 = no. of chairs in all 7 long rows.
y = no. of chairs stacked.
Total no. of chairs = 18x+7x+126+y = 25x+y+126











Subtract the two equations:



, substitute in 11x+y=126

11(9)+y=126
99+y=126
y=27

9 chairs in each short row and 27 chairs stacked.

(a) 

(b) 7x+126 = 7(9)+126 = 189 in all 7 long rows.

Edwin
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