Word Problem.

Question

the admission fee at a small fair is $1.50 for children and $4.00 for adults. on a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

Answer 1

Sadiya,

 

This problem requires using two equations, the first is the total number of tickets sold, and the second is how much those tickets were sold for.

 

First, lets setup the variables.

 

C=1.5

A=4

 

C+A=2200  [Total number of tickets sold]      Now you need to modify one equation to cancel a variable.  

 1.5C+4A=5050 [Total value of tickets sold]    I chose to multiply the first by -1.5

-1.5C-1.5A=-3300  [Now add the equations]

   0C+2.5A=1750   [Next, solve for A]

              A=1750/2.5

              A=700    [There were 700 Adult tickets sold]

C+A=2200   [Substitute 700 for A in this equation]

C+700=2200     [Solve for C]

C=1500.

 

So, on this day, 700 Adults bought tickets for $4 and 1500 children bought tickets for $1.5, for a total of 2200 tickets an $5050.

 

Hope this helps.