How many adult admissions were collected?

Question

At a? museum, adult admission is $13.75 and children admission is $6.25. During one? day, a total of 2300 adult and children admissions were? collected, and $24,875 in admission fees was collected. How many adult admissions were? collected?

Answer 1

a = # adults

c = # children

 

equation 1)  a + c = 2300       2300 tickets were sold

equation 2)  13.75a + 6.25c = 24,875     $24,785 in fees collected

 

From equation 1 a = -c + 2300

Substitute that in place of a in equation 2

 

13.75(-c+2,300) + 6.25c = 24,875

-13.75c + 31,625 + 6.25c = 24,875

-7.5c + 31,625 = 24,875

-7.5c = 24,875-31,625

-7.5c = -6750

c = -6750/(-7.5)

c = 900

 

a = 2300-c = 2300-900=1400

 

1400 adult tickets were sold

900 children tickets were sold

 

Check:  13.75a + 6.25c = 24875

13.75(1400) + 6.25(900) = 24875

24875=24875

Equation balances.