SOLUTION: include systems of equations for solving
Adult tickets for a play cost $14 and child tickets cost $3. If there were 26 people at a performance and the theater collected $199 fr
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Adult tickets for a play cost $14 and child tickets cost $3. If there were 26 people at a performance and the theater collected $199 fr
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Question 124080: include systems of equations for solving
Adult tickets for a play cost $14 and child tickets cost $3. If there were 26 people at a performance and the theater collected $199 from tickets, how many adults and how many children attended the play? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Adult tickets for a play cost $14 and child tickets cost $3. If there were 26 people at a performance and the theater collected $199 from tickets, how many adults and how many children attended the play?
:
Let a = no. of adults
and
Let c = no. of children
:
Write an equation for each statement/phrase:
"If there were 26 people at a performance"
a + c = 26
Subtract a from both sides:
c = (26-a); we can use this for substitution:
:
"Adult tickets for a play cost $14 and child tickets cost $3...the theater collected $199 from tickets,"
14a + 3c = $199
:
how many adults and how many children attended the play?
:
Substitute (26-a) for c in the above equation, find a
14a + 3(26-a) = 199
14a + 78 - 3a = 199
14a - 3a = 199 - 78
11a = 121
a =
a = 11 adults
:
We know c = (26-a); substitute 11 for a
c = 26 - 11
c = 15 children
:
:
Check solutions in the $$ equation
14a + 3c = $199
14(11) + 3(15) =
154 + 45 = 199; confirms our solutions
