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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

$386$ $386$ were senior citizens

Explanation:

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

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

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

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

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

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

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

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