Find the total attendance for the play.

Question

The attendance for the first night of a school play is 1/4 the total attendance. The attendance for the second night is 30 more than 1/5 of the attendance. The attendance for the third night is 2/7 of the total attendance. The last night has an attendance of 340 people. Find the total attendance for the four night of the play.

Answer 1

Let t = total attendance for the 4 nights of the play

 

The first night: t/4

 

The second night: 30 + t/5

 

The third night: 2t/7

 

The fourth night: 340

 

Total attendance for all 4 nights: t

 

t = t/4 + 30 + t/5 + 2t/7 + 340

 

combine like terms, find a common denominator 4*5*7 = 140

 

t = 370 + 35t/140 + 28t/140 + 40t/140

 

t = 370 + 103t/140

 

multiply everything by 140

 

140t = 51,800 + 103t

 

140t - 103t = 51,800

 

37t = 51,800

 

divide both sides by 37

 

t = 1,400