The Family Fine Arts Center charges $21 per adult and $15 per senior citizen for its performances. On
a recent weekend evening when 523 people paid
admission, the total receipts were $8979. How
many who paid were senior citizens?

334 seniors

Step-by-step explanation:

First, to tell apart the admissions for adults and seniors, use the variables x for adults and y for seniors.

If there was a combined total of 523 people, then you know that the combined amount of adults and seniors is:

x + y = 523

If there was a combined total cost of $8979, then you know that the combined amount of admission costs is:

21x + 15y = 8979

Then you solve the system of equations (see IMAGE.A):

First, solve for x:

21x + 15y = 8979

21x = –15y + 8979

x = y +

Then, plug in the x-value to the other equation to find the y-value:

x + y = 523

y + + y = 523

y +  = 523

y =

y = ()

y = 334

This means that there were 334 seniors who paid.

Step-by-step explanation:

Cone Volume = (π • r² • h) ÷ 3

109.9 = PI * 5 * radius^2 / 3

3* 109.9 / (3.14 * 5) = radius^2

329.7 / 15.7

radius^2 = 21

radius = 4.582575695