1000 tickets were sold. Adult tickets cost $8.50, children's tickets cost $4.50, and a total of $7300 was collected. How many tickets of each kind were sold?

2 Answers
Sep 8, 2015

Answer:

Adult# =700#
Children#=300#

Explanation:

#a = #Adult
#c=#Children

Then-

#a+c=1000# ---------------------------(1)
#8.50a+4.50c = 7300#-----------(2)

Solve the equation (1) for c
#c = 1000-a#
Substitute the value of c in equation (2)
#8.50a+4.50(1000-a) = 7300#
#8.50a+4500-4.50a) = 7300#
#4a = 7300-4500 = 2800#
#a=2800/4=700#

Substitute the value of a in equation (1)

#700+c=1000#
#c=1000-700=300#

Sep 8, 2015

Answer:

#700# adult tickets and
#300# children's tickets

Explanation:

Define:
#color(white)("XXX")a = "number of adult tickets"#
#color(white)("XXX")c = "number of children's tickets"#

We are told:
[1]#color(white)("XXX")a+c=1000#
and
[2]#color(white)("XXX")850a+450c=730000#

Simplifying [2] by dividing by #50#
[3]#color(white)("XXX")17a+9c=14600#

Multiply [1] by 9
[4]#color(white)("XXX")9a+9c=9000#

Subtract [4] from [3]
[5]#color(white)("XXX")8a = 5600#

Divide by #8#
[6]#color(white)("XXX")a = 700#

Substitute #700# for #a# in [1] and simplify
[7]#color(white)("XXX")c=300#