The little Town Fine Arts Center charges $21 per adult and $10 per senior citizen for its performances. on a recent weekend evening when 559 people paid admission, the receipts were $7493. How many who paid were senior citizens?

1 Answer
Nov 8, 2016

#386# were senior citizens

Explanation:

Let #a# be the number of adult paid admissions
and #s# be the number of senior paid admissions.

We are told
[1]#color(white)("XXX")a+s=559#
and
[2#color(white)("XXX")21a+10s=7493#

We could rearrange [1] as
[3]#color(white)("XXX")s=559-a#

Then substituting #(559-a)# for #s# in [2]
[4]#color(white)("XXX")21a+5590-10a=7493#

[5]#color(white)("XXX")11a= 1903#

[6]#color(white)("XXX")a=173#

The substituting #173# for #a# in [3]
[7]#color(white)("XXX")s=559-173= 386#