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?

Question

Julia Adams · Accepted Answer

#386# were senior citizens

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#

Eva Abramson · Answer

undefined There were 347 senior citizens who paid admission.

Julia Adams · Answer

undefined Let $ x $ be the number of adults and $ y $ be the number of senior citizens.

Given:
$$ x + y = 559 $$
$$ 21x + 10y = 7493 $$

Solving these equations simultaneously:
$$ x = 559 - y $$
$$ 21(559 - y) + 10y = 7493 $$
$$ 11739 - 21y + 10y = 7493 $$
$$ -11y = -4246 $$
$$ y = 386 $$

Therefore, there were 386 senior citizens who paid admission.