452 seats $58 for adults & $16 for kids. Total was $15,380. how many of each type of tickets were sold?

Question

A theatre contains

452 seats and the ticket prices for a recent play were

​$58 for adults and ​$16 for children. If the total proceeds were

​$15,389 for a​ sold-out matinee, how many of each type of ticket were​ sold?

Answer 1

Here are the facts:

452 seats

$58 per Adult

$16 per Child

Total amount = $15,380

Here's your set up:

x + y = 452

58x + 58y = $15,380

Here's the solution:

x + y = 452

-x = -x

y= 452 - x

58x + 16(452 - x) = 15,380

58x + 7,232 - 16x = 15,380

(58x - 16x) + 7,232 = 15,380

42x + 7,232 = 15,380

-7,232 = -7,232

42x = 8,148

------- ---------

42 42

x = 194

y = 492 - 194

y = 258

Double Check:

58(194) + 16 (258) = 15,380

11,252 + 4,128 = 15,380

15,380 = 15,380 -- TRUE

Answer 2

Hi :)

This is what you were given:

452 total number of seats

$58 adult price

$16 kids price

$15,380 total proceeds

First you have to set up your variables. Say:

x= # adult tickets sold

then 452-x= # kids tickets sold

Now you set up the equation using the variables above and multiplying them how the cost of each type of ticket:

58(x) + 16(452-x) = 15,380

Use distributive property to solve.

58x + 7232 - 16x = 15,380

Combine like terms

42x + 7232 = 15,380

Solve for x by isolating it to one side

42x= 15,380 - 7232

42x= 8,148

x= 8,148/42

x= 194

Above we set x to the # adult tickets sold. So if 194 adult tickets sold them 452-194= 258 kids tickets sold.

Answer: 194 adult and 258 kids tickets sold.

Hope this helps!