SOLUTION: A church group goes to the movies every Friday night. Last week, they bought 26 adult tickets and 40 youth tickets, at a total cost of $408. This week, they spent $369 on 18 adult

Question 1055816: A church group goes to the movies every Friday night. Last week, they bought 26 adult tickets and 40 youth tickets, at a total cost of $408. This week, they spent $369 on 18 adult tickets and 45 youth tickets. Find the cost of one adult ticket and one youth ticket?
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
adult=x youth =y
26x+40y=408
18x+45y=369
multiply top by 9 bottom by -8 to eliminate y
-234x-360y=-3672
144x+360y=2952
-90x=-720
x=8
y must equal 208+40y=408; 40y=200, y=5
check in second equation
144+225=369
adult tickets are $8
youth tickets are $5
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

A church group goes to the movies every Friday night. Last week, they bought 26 adult tickets and 40 youth tickets, at a total cost of $408. This week, they spent $369 on 18 adult tickets and 45 youth tickets. Find the cost of one adult ticket and one youth ticket?

Let number of adults' and youth tickets be A an Y, respectively
Then we get the following PROCEEDS equation for last week: 26A + 40Y = 408____2(13A + 20Y) = 2(204)______13A + 20Y = 204 ------ eq (i)
We also get the following PROCEEDS equation for this week: 18A + 45Y = 369____9(2A + 5Y) = 9(41)_____2A + 5Y = 41 ------ eq (ii)
Now, multiply eq (ii) by - 4 to get eq (iii), an equation with OPPOSITE-SIGNED, but SIMILAR coefficients on Y.
Add eqs (iii) & (i) to get the value of A, as Y was eliminated when eqs (iii) & (i) were added
Substitute value for A in a REDUCED eq (ii) to get value of Y, or cost of 1 youth's ticket.
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