Question

Tickets to a concert cost either $12 or $15. A

total of 300 tickets are sold, and the total
receipts were $4,140. How many of each kind
of ticket were sold?
First complete the equations below, where x stands for
$12 tickets and y stands for $15 tickets.
[?]x + [ ]y = 4,140; x + y = U

Answer 1

Answer: tickets: 120………180

Explanation:

Answer 2

• 12x +15y = 4140; x + y = 300
• x = 120; y = 180

Explanation:

The first equation is for receipts. Each x ticket generated $12 in receipts, so the first term needs to be 12x. Each y ticket generated $15 in receipts, so the second term needs to be 15y. U in this set of equations is the total number of tickets, said to be 300.

The equations are ...

12x +15y = 4140; x +y = 300

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Using the second equation to write an expression for x, we have ...

x = 300 -y

Substituting this into the first equation gives ...

12(300 -y) +15y = 4140

3600 +3y = 4140

y = (4140 -3600)/3 = 180

x = 300 -180 = 120

The number of tickets sold is ...

$12 tickets -- 120

$15 tickets -- 180

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You might want to notice that the equation we ended up with:

4140 -12(300) = 3y

is equivalent to this "word solution." This can be done in your head; no equations required.

If all the tickets sold were $12 tickets, the revenue would be $3600. The revenue is $540 more than that. Each $15 ticket generates $3 more revenue than a $12 ticket, so to have $540 more revenue, we must have 540/3 = 180 $15 tickets.