Question

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?

Answer 1

`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`