At the city museum, child admission is $6.10 and adult admission is $9.30. On Friday, 163 tickets were sold for a total sales of $1311.10. How many child tickets were sold that day?

Answer 1

Hi, Marlon,

At first glace, this seems impossible. But wait a minute - we have two unknowns, yes, but we also have two equations. Let's see if this will work.

I have a chart with the answer already, but it is useful to look at it while we do the work.

Let x = the number of child tickets at $6.10 each. Total sales from the child tickets is thus x*6.10.

Let y = the number of adult tickets at $9.30 each. Total adults sales is thus y*9.30.

An equation for total sales would be x*6.10 + y*9.30 = $1,311.10.

But we also know the number of total tickets is 163. That means we have the equation x + y = 163.

AHA! Two equations and 2 unknowns. There's got to be a way . .[dramatic beat] .

Rearrange: x = 163 - y

Substitute: (163-y)*6.10 + 9.30*y = 1,311.1

994.3 - 6.10y + 9.30y = 1,311.1

994.3 + 3.2y = 1,311.1

3.2y = 316.80

y = 99 WOW! An exact number, so I'm encouraged.

If y = 99: then x = 163 - 99 = 64.

That's a total of 163 tickets. 99 at $9.30 each = $920.70

and 63 at $6.10 each = $390.40

The total is [drum roll please . . .] = $1,311.10

[insert smiley]

I hope this helps. It was fun,

Bob

Answer 2

Hello, Marlon

Okay, so let's let x = the number of child admissions sold

Then the number of adult admissions sold is 163 - x

So now we can put that into an equation.

6.10x + 9.30(163-x) = 1311.10

Now, just solve for x:

6.10x + 1515.9 - 9.3x = 1311.10

-3.2x = - 204.8

x = -204.8/-3.2

x = 64

So there were 64 children's tickets sold.

(the number of adult tickets sold would be 163 - 64 = 99)

Answer 3

To solve this problem with 2 variables (the number of adult tickets and the number of child tickets) we need to set up two equations.

First we will define our variables:

x = number of adult tickets

y = number of child tickets

Then we will set up our equations:

1) Number of tickets

number of adult tickets + number of child tickets = total number of tickets

We can write this equation using our variables and the total from the problem as:

x+y = 163

2) Total Sales

(number of adult tickets x price of an adult ticket) + (number of child tickets x price of a child ticket) = total sales

We can substitute in our variables and the prices which are given in the problem:

(x*9.3) + (y*6.1) = 1311.1

Using our two equations we can solve for our two variables, x and y.

1) x + y = 163

x = 163 - y

2) 9.3x + 6.1y = 1311.1

9.3(163 - y) + 6.1y = 1311.1

1515.9 - 9.3y + 6.1y = 1311.1

204.8 = 3.2y

y = 64

Therefore 64 child tickets were sold. This value can also be plugged back into the first equation to find the number of adult tickets sold.

Answer 4

Let c=the # of child tickets sold Cost of child admission: $6.10

Let a=the # of adult tickets sold Cost of adult admission: $9.30

Total tickets sold = 163 Total sales: $1311.10

Set up 2 equations

# child tickets sold + # adult tickets sold = total tickets sold

c + a = 163

Subtract a from both sides to get

c = 163 - a

revenue from child ticket sales + revenue from adult ticket sales = total sales

6.10c + 9.30a = 1311.10

Substitute value for c in terms of a

6.10(163 - a) + 9.30a = 1311.10 Distribute 6.10 to get

(994.3 - 6.10a) + 9.30a = 1311.10 Combine like terms to get

994.3 + 3.2a = 1311.10 Subtract 994.3 from both sides to get

3.2a = 316.8 Divide both sides by 3.2

a = 99

c = 163 - a

c = 163 - 99

c = 64

64 child tickets were sold that day

Answer 5