admission costs $7 for adults and $4 for children. one day $730 was collected in admissions for 142 individuals. how many children attended?

Question

admission costs $7 for adults and $4 for children. one day $730 was collected in admissions for 142 individuals. how many children attended?

Answer 1

Hi Devan,

This is a "systems of equations" problems - you will end up with 2 equations that have to have the same solution.

 

Need a variable for the number of Adult tickets (A) and a variable for the number of Children tickets (C).  

 

1st Equation:  Everyone needs a ticket. 

 

There are only Adult  tickets and Children  tickets.  And 142 people came.  So...

 

A + C = 142

 

 

2nd Equation:  the money

 

7A is the money from the Adult tickets ($7 per Adult ticket * A adult tickets)

4C is the money from the Children tickets sold ($4 per Children ticket * C children tickets)

 

The total money had to come from all the tickets sold, so...

 

7A + 4C = 730

 

 

This word problem results in the system of equations:

 

A + C = 142

7A + 4C = 730

 

 

Solve the first one for A:   A = 142 - C

 

Substitute this into the bottom equation:

 

7(142 - C) + 4C = 730

 

 

Distribute the 7 into the parenthesis

 

994 - 7C + 4C = 730

 

Combine like terms

 994 - 3C = 730

 

Add 3C to both sides.

 

994 = 730 + 3C

 

Subtract 730 from both sides

 

264 = 3C

 

Divide both sides by 3

 

C = 88

 

So 88 children tickets were sold, so 88 children attended.