SOLUTION: James' school is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 6 adult tickets and 7 child tickets for a total of $155. The school to

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: James' school is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 6 adult tickets and 7 child tickets for a total of $155. The school to      Log On


   

Question 1156418: James' school is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 6 adult tickets and 7 child tickets for a total of $155. The school took in $258 on the second day by selling 8 adult tickets and 14 child tickets. What is the price each of one adult ticket and one child ticket?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost of an adult ticket
Let +b+ = the cost of a child ticket
---------------------------------------------
(1) +6a+%2B+7b+=+155+
(2) +8a+%2B+14b+=+258+
--------------------------------
Multiply both sides of (1) by +2+ and
subtract (2) from (1)
(1) +12a+%2B+14b+=+310+
(2) +-8a+-+14b+=+-+258+
----------------------------------
+4a+=+52+
+a+=+13+
and
(1) +6a+%2B+7b+=+155+
(1) +6%2A13+%2B+7b+=+155+
(1) +7b+=+155+-+78+
(1) +7b+=+77+
(1) +b+=+11+
------------------------
$13 = the cost of an adult ticket
$11 = the cost of a child ticket
--------------------------------------
check:
(2) +8a+%2B+14b+=+258+
(2) +4a+%2B+7b+=+129+
(2) +4%2A13+%2B+7%2A11+=+129+
(2) +52+%2B+77+=+129+
(2) +129+=+129+
OK

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

James' school is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 6 adult tickets and 7 child tickets for a total of $155. The school took in $258 on the second day by selling 8 adult tickets and 14 child tickets. What is the price each of one adult ticket and one child ticket? 
Let cost of each adult's ticket be A, and each child's child's, C

We then get: 6A + 7C = 155 ------ eq (i)

Also, 8A + 14C = 258____2(4A + 7C) = 2(129)_____4A + 7C = 129 ------- eq (ii)

2A = 26 ------ Subtracting eq (ii) from eq (i)

A, or 

You should now be able to find the cost of a child's ticket!