240 Chair Arrangment

Question

Emily was arranging seats for an event. She needs to seat 240 people. Her idea had 4 more chairs per row but used 2 less rows. How many chairs were in each row for Emily's plan?

Answer 1

*** Update -- I believe since this

is an elementary math problem,

they just wanted you to experiment

with the numbers a bit to come up

with the answer. What I showed

below is how to solve it using math. ***

This is an interesting problem,

but think this is a bit more

difficult than elementary math.

Let c = number of chairs in row

and r = # rows

So c*r = 240. (Original seating)

Emily proposed 4 more in each

row, but 2 less rows.

(c+4)(r-2) = 240

Multiply this out and solve

for c (use FOIL method)

c*r - c*2 +4*r -4*2 = 240

cr -2c +4r - 8 = 240

but cr = 240, so

substitute

240 -2c + 4r - 8 = 240

-240 -240 Subtract 240 from both sides

-------------------------------

-2c + 4r - 8 = 0

+2c +2c Add 2c to both sides

------------------------

4r - 8 = 2c

-------- ----- Divide both sides by 2

2 2

2r -4 = c

Plug this into cr = 240

(2r-4)r = 240

2r² - 4r = 240

-240 -240 subtract 240 from both sides

---------------------'

2r² - 4r - 240 = 0

----------------- ------ Divide both sides by 2

2 2

r² -2r -120 = 0

factor

(r - 12)(r + 10) = 0

r - 12 = 0 or r + 10 = 0

+12 +12 -10. -10

-------------- ----------------

r = 12 or r = -10

Can't have a negative

number of rows, so

r =12.

Plug in to find c

cr = 240

c(12) = 240

-------- ------ Divide both sides by 12

12 12

c = 20

Original plan was

12 rows and 20 chairs

In each row

Emily's plan was 4 more

chairs and 2 less rows.

10 rows, 24 chairs in row