240 Arrangment of chairs

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

rows times number per row = total chairs

rn = 240

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

rn-2n+4r -8 = 240

rn-2n+4r = 248

rn = 240

subtract to get

4r-2n = 8

2r-n = 4

n=2r-4

r(2r-4) = 240

2r^2 -4r =240

divide by 2 and complete the square

r^2 -2r +1 = 120+1

r-1 = sqr121

r = 1+11 = 12 rows

n= 2r-4 = 2(12)-4 = 20 chairs per row

12(20) = 240

then she reduces rows by two and increases chairs per row by four

(12-2)(20+4) = 10(24) = 240 total chairs

her plan is to have 24 chairs per row