SOLUTION: The Arcadia Theater charges $4 for adult tickets and $3 for student tickets. Josh purchased 9 tickets (some students and some adults) for $31. Write a systems of equations used to
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Question 1114236: The Arcadia Theater charges $4 for adult tickets and $3 for student tickets. Josh purchased 9 tickets (some students and some adults) for $31. Write a systems of equations used to find a, the number of adult tickets, and s, the number of student tickets Josh purchased.
Find the cost of ticket for each student and adult as well.
I do not understand how I am supposed to solve this problem. Do I write the system of equation as
4a*9=31
3s*9=31
Thanks for your help!
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) a + s = 9
:
2) 4a + 3s = 31
:
solve equation 1 for a
:
a = 9 - s
:
substitute for a in equation 2
:
4(9 - s) + 3s = 31
:
36 - 4s + 3s = 31
:
-s = -5
:
s = 5
:
a = 9 - 5 = 4
:
************************************************************
Josh bought 4 adult tickets and 5 student tickets
:
check answer with equation 2
:
4(4) + 3(5) = 31
:
16 + 15 = 31
:
31 = 31
:
our answer checks
:
from equation 2, we see that
:
Josh spent $16 on adult tickets and $15 on student tickets
************************************************************
:
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.
It is a standard ticket problem.
Read the lessons
- Using systems of equations to solve problems on tickets
- Three methods for solving standard (typical) problems on tickets
in this site.
Learn from these lessons on how to solve such problems once for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
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