Answer:
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 = [tex]-\frac{15}{21}[/tex]y + [tex]\frac{8979}{21}[/tex]
Then, plug in the x-value to the other equation to find the y-value:
x + y = 523
[tex]-\frac{15}{21}[/tex]y + [tex]\frac{8979}{21}[/tex] + y = 523
[tex]\frac{2}{7}[/tex]y + [tex]\frac{8979}{21}[/tex] = 523
[tex]\frac{2}{7}[/tex]y = [tex]\frac{668}{7}[/tex]
y = [tex]\frac{668}{7}[/tex] ([tex]\frac{7}{2}[/tex])
y = 334
This means that there were 334 seniors who paid.
