A theater sold a total of 240 tickets for a show, some of which were adult tickets and the rest child tickets. An adult ticket cost $15 and a child ticket cost

Question

An adult ticket cost $15 and a child ticket cost $9. If the total ticket sales amounted to $3060, construct a solve a system of equation to find how many of each type of ticket were sold. Thank you please help me set up.

Answer 1

Dear Roseland:

 

I answered this question for you a couple of days ago.  Here it is again:

 

Let NA be the number of adult tickets sold and NC be the number of child tickets sold.

We know that NA + NC = 240. (Eq. 1)

We also know that ($15)*NA + ($9)NC = $3060. (Eq. 2)

We have a choice of how to proceed. We can either solve Eq. 1 for NA and substitute that value into Eq. 2, or we can solve Eq. 1 for NC and substitute that value into Eq. 2.

Let's do it the first way mentioned:

NA = 240 - NC

Eq. 2 then becomes:

($15)(240 - NC) + ($9)(NC) = $3060

We now have one equation with one unknown (NC).

($15)(240) - ($15)(NC) + ($9)(NC) = $3060

$3600 - 6NC = $3060

-6NC = -$540

NC = 90

If NC = 90, then NA = 240 - 90 = 150

Let's see if our answer makes sense:

Does (NC)($9) + (NA)($15) = $3060?

Does (90)($9) + (150)($15) = $3060?

YES!

12/13/2013 | William S.

Answer 2

Hey Roseland -- we may start "simple" ... pretend all 240 tickets sold are $15 ...

 

total sales would be $3600 -- that's $540 too much ... "trade in" $9 tickets for the $15 ones ...

 

the $6 difference "traded in" 90x corrects the $540 "overshoot" ... 150A, 90C works, ma'am :)

Answer 3

When solving any word problem, I like to focus on what I know, and let those details lead us to what we don't know.   

I know that the total ticket sales amount is $3060 and that this is the sum of adult ticket sales (a) plus child ticket sales (c).  Therefore:

3060 = a + c

 

I also know that to calculate adult ticket sales, you need to multiple total number of adult tickets sold (x) multiplied by the price of each ticket adult ticket.  If we look at the question, we see that the price of each ticket is $15.  Therefore:

a = x * 15

 

Now, let's modify our first equation substituting for "a".

 

3060 = (x * 15) + c

 

Calculating the total child ticket sales amount is the same as the adult.  The total child ticket sales  amount is the total number of child tickets sold (y) multiplied by the price of each child ticket. If we look at the question, we know that the cost of each child ticket is $9.  therefore:

 

c = y * 9.

 

Now let's substitute c in our modified equation. 

3060 = (x * 15) + (y * 9).

 

Since we know that multiplication comes first in the order of operations, we can actually drop the parenthesis if we like.  Leaving.

 

3060 = x * 15 + y * 9

 

 

 

 

 

 

 

 

 

 

 

Answer 4

You need two equations. One tells you the total number of tickets (240) sold to both adults and children.

If A =adult and C = child, then A + C = 240 is the first equation.  

For the second equation, you have the total ticket sales ($3060) and the cost of the sale for each adult ($15 x A) and each child ($9 x C).  So, your second equation is: 15A +9C = 3060.

Here are your two equations written on top of each other:

A + C = 240

15A + 9C = 3060

 

I did that so you can see how to get rid of either A and get the solution for C, or visa versa.

If you multiply the top equation by 15, you get:

15A + 15C = 3600

 

Now subtract the two equations:

  15A + 15C = 3600

-15A   -  9C =  -3060 (subtraction changes all the signs)

_______________

              6C  = 540

 

Now you should be able to solve for C. With that information, you can use the first equation to solve for A. If you get stuck, let me know.

Answer 5

X - adult ticket sold

 240 - X = children ticket sold

 

X ( 15 ) + ( 240 - X) 9= 3060 (***)

 

 15X + 240(9) -9x  = 3060

 

  6X = 900

 

  X = 150 - Number of adult ticket sold

 

  240 -150 =90 - number of child ticket sold.

Answer 6

Let number of adult tickets sold be x

and let number of child tickets sold be y

 

Total tickets sold = 240

so x + y = 240

Total ticket sale = 3060

so 15x + 9y = 3060

 

Solve these two simultaneous equations

x = 240 - y

substitute value of x in second equation

15(240 - y) + 9y = 3060

3600 - 15 y + 9y = 3060

- 6y = -540

y = 90

substitute value of y in first equation

x + 90 = 240

x = 150

 

Verify

 

substitute value of x and y in second equation

 

15(150) + 9(90) = 3060

2250 + 810 = 3060

3060 = 3060 so value of x and y are correct

Therefor number of adult tickets sold = 150

and number of child tickets sold = 90

:)

 

Answer 7

Good morning! While work type problems can seem overwhelming, the idea is to go through one piece at a time. While 240 tickets (both adult and child) were sold, you do not know how many of each. However you do know that adult tickets + children tickets = 240

 

In math you can represent an unknown factor with a variable (usually x). Let's use x to represent the number of adult tickets. Therefore you could say the following:

 

x + children tickets = 240

 

subtract x from both sides : (x + children's tickets) - x = 240 - x and you get:

 

children tickets = 240-x

 

Now look at the money.

 

$15(x) + $9(240-x) = $3060

$15x + $2160 - $9x = $3060

 

combine like terms (the x's):

 

$6x + $2160 =$3060

 

now subtract $2160 from both sides ($6x + $2160 - $2160 = $3060 -$2160):

 

$6x = $900

 

Now divide both sides by $6 ($6x/$6 = $900/$6)

 

x=150

 

Now go back again to the equation for children tickets above (children tickets = 240 - x) and plug in the value for x:

 

children tickets = 240-150 = 90

 

Therefore 150 adult tickets and 90 children tickets were sold

 

Hope this helps

 

Mike