Algebra written questions please help!

Question

If 71 people attend a concert and tickets for adults cost $3 while tickets for children cost $2.5 and total receipts for the concert was $194.5, how much of each went to the concert?    ____ adults. ____children.

Answer 1

x = number of adults

 

y = number of children

 

x + y = 71         first equation

 

3x + 2.5y = 194.50    second equation

 

substitute y = 71 - x into second equation

 

3x + 2.5(71 - x) = 194.50

 

3x + 177.5 - 2.5x = 194.50

 

.5x = 17

 

x = 34

 

so y = 71 - 34 = 37

 

34 adults and 37 children

 

 

Answer 2

Simultaneous equations!  Two unknowns require two equations!

 

Let c = # of children

Let a = # of adults

 

c + a = 71    Therefore, c = 71 - a  equation number 1

 

(a)($3) + (c)($2.5) = 194.50   equation number 2

 

Substitute: 3a + (2.5)(71-a) = 194.50

Simplify:  3a + 177.5 - 2.5a = 194.50

Combine like terms:  .5a = 17

 

a = 34  c= 37