SOLUTION: Tickets for a certain show cost ​$18​, ​$25​, ​or, for VIP​ seats, ​$39. If tenten times as many ​$18 tickets were sold as VIP&#8203

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Question 1115924: Tickets for a certain show cost ​$18​, ​$25​, ​or, for VIP​ seats, ​$39. If tenten times as many ​$18 tickets were sold as VIP​ tickets, and the number of ​$18 tickets sold was 56 more than the sum of the number of ​$25 tickets and VIP​ tickets, sales of all three kinds of tickets would total ​$54,988. How many of each kind of ticket would have been​ sold?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x of the $18 tickets
y of the $25 tickets
z of the $39 VIP tickets

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If tencross%28ten%29 times as many ​$18 tickets were sold as VIP​ tickets, and the number of ​$18 tickets sold was 56 more than the sum of the number of ​$25 tickets and VIP​ tickets, sales of all three kinds of tickets would total ​$54,988.
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system%28x%2Fz=10%2Cx=y%2Bz%2B56%2C18x%2B25y%2B39z=54988%29

If take x=10z and substitute for x, then ....

.
.
system%289z-y=56%2C219z%2B25y=54988%29

25*E1,
system%28225z-25y=1400%2C219z%2B25y=54988%29

highlight%28z=127%29-------number of VIP tickets

highlight%28x=1270%29------number of $18 tickets

highlight%28y=1087%29-------number of $25 tickets
.