Ticket sale calculation

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Ticket sale calculation

Postby barnamah » Sat 09 April, 2011 13:16

A theater sells adult tickets for $10 and child tickets for $7.50. If the theater sells 1000 tickets for a Saturday, and it's total for that day was $9672.50, how many of each type of ticket did the theater sell for that day?
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Re: Ticket sale calculation

Postby Integr88 » Sat 09 April, 2011 14:14

let adult be A and child be C so we have
Tickets for:
A=$10.00
C=$7.50

the total ticket sale is $9672.50 so we can write the sale equation as:
`10A+7.5C=9672.50` (EQ1)

we know the total of tickets are 1000 so we have
A+C=1000 (EQ2).
so we have 10A and A to solve for C we can multiply EQ2 by -10 and we have:
-10A-10C=-10000 (EQ3)

Subtracting EQ2 from EQ1 we can write:
`10A+7.5C=9672.50`
`-10A-10C=-10000`
------------------------
`0 -2.5C= - 327.5`
now we have `-2.5C= - 327.5` and dividing both side by -2.5 looks `(-2.5C)/-2.5= - 327.5/-2.5` the -2.5 on the left cancels out and we have:
`C= - 327.5/-2.5=131`
so the number of child ticket is `131`

now subbing the 131 into our EQ2 we have
`A+131=1000`
Subtract 131 from both side `A+131-131=1000-131` and we left with
`A=1000-131=869`

so A=869 which tells us 869 adult tickets were sold

`:.` 131 Child tickets and 869 adult tickets sold so the total 131+869=1000
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