How would you solve this: Tickets for a community dinner cost $4 for adults and $3 for children. A total of 390 tickets was sold ,earning $1,380. how many of each type of ticket were sold?

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20-11-2014
Mathematics

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How would you solve this: Tickets for a community dinner cost $4 for adults and $3 for children. A total of 390 tickets was sold ,earning $1,380. how many of each type of ticket were sold?

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TheKingHami TheKingHami · Answer 1 · 2014-11-20T20:40:49-05:00

We can make a system of equations to solve for this.
We'll use the variable a for adult ticket costs and c for children ticket costs.

4a+3c=1380 (cost of adult plus child tickets)
a+c=390 (number of child tickets plus adult tickets)

Now we can use substitution or elimination. I'll be using substitution since we already have singular variables in the second equation.

First we isolate a variable.
a+c=390
a=390-c

Now we plug in and solve

4(390-c)+3c=1380
1560-4c+3c=1380
-c=-180
c=180

Now we know that there were 180 children tickets sold. We could do the same thing to find the amount of adult tickets but we already know that there were a total of 390 tickets sold. So if there are 180 child tickets, the rest have to be adult tickets. 390-180=210

180 Children tickets
210 Adult tickets