At the city museum, child admission is $6.00 and adult admission is $9.60 . On Friday, 143 tickets were sold for a total sales of $1164.00

Question

how many adult tickets were sold

Answer 1

Problems like this require constructing two formulas.  Typically, one is a simple sum, and the other shows the relationship between the two variables.

 

Let c=  the number of child admissions sold

Let a = the number of adult admissions sold

 

It is given that the total of all tickets is 143; therefore...

 

a + c = 143  (We'll call that equation #1)

 

We also know that the total money collected is $1164.  That is the sum of all the money collected for child admissions PLUS all the money from adult admissions.

 

The expression for the total cost of any item is the cost per ticket (in this case) times the number of tickets.  Therefore:

 

6.00c + 9.60a = 1164  (We'll call this equation #2)

 

Now we have an ordinary system of equations problem.  You probably know what to do from here, but I'll proceed...

 

Solve equation #1 for c by subtracting a from both sides:

 

c = 143 - a

 

Now, we have an expression for c, which we can substitute into equation #2:

 

6 ( 143 - a) + 9.60a = 1164

 

We now have an equation in one variable.  Yay!

 

858 - 6a + 9.60a = 1164 (distributive property)

 

-6a + 9.60a = 306 (subtraction property)

 

3.6 a = 306 (combine like terms)

 

a = 85 (division property)  

 

85 adult tickets were sold (ANSWER)

 

If we were to substitute this value into equation #1, we would also learn that 58 child tickets were sold.