Question

In a theater, there are 4 long rows of chairs,each with an equal number of chairs There are 5 ahort rows of chairs,each with an equal number of chairs On a crowded day, the ushers added 2 chairs to each long row and 3 chairs to each short row if x represents the number of chairs in each long row and y represents the number of chairs in each short row,the total number of chairs in the theater is given by the expression 2)Sly 3) An equivalent expression is

Answer 1

An equivalent expression is 4x + 5y + 23

Explanation:

There are 4 long rows of chairs and 3 short rows of chairs.

Let x be the number of chairs in long rows and y in short rows.

So total number of chairs in theater

C = 4x + 5y

Now on a crowded day 2 chairs were added in long rows so number of chairs in long rows becomes

= 4 (x + 2)

Similarly ushers add 3 chairs add in short rows so total number of chairs in short row = 5 ( y + 3 )

Now total chairs in theater

C' = 4 ( x + 2 ) + 5 ( y + 3 )

= 4x + 8 + 5y + 15

= 4x + 5y + 23

C' = C + 23 [Since C = ( 4x + 5y ) ]

Number of chairs added were 23 as compared to normal days.

Answer 2

There are 4 long rows and 5 short rows in the theater. x represents the number of chairs in each long row and y represents the number of chairs in each short row.

So, total number of chairs in 4 long rows= 4x
Total number of chairs in 5 short rows = 5y
Total number of chairs in the theater on a normal day = 4x + 5y

When 2 chairs are added to each long row, the number of chairs will change to (x+2).
So, total number of chairs in 4 long rows will be = 4(x+2)

When 3 chairs are added to each short row, the number of chairs will change to (y+3)
So, total number of chairs in 5 short rows will be = 5(y+3)

Thus, total number of chairs in the theater in rush day = 4(x+2) + 5(y+3)
= 4x + 8 + 5y + 15
= 4x + 5y + 23

Thus we can say the number of chairs increase by 23 as compared to a normal day.