Help please?

Question

For a Saturday matinee, adult tickets cost $4.50 and kids under 12 pay only $3.00. If 70 tickets are sold for a total of $285, how many of the tickets were adult tickets and how many were sold to kids under 12?

Answer 1

Hi Samantha.

 

Let's set up some variables.

 

A = the number of adult tickets sold

K = the number of kid tickets sold

 

Ca = Cost of an adult ticket, which is $4.50

Ck = Cost of a kid's ticket, which is $3.00

 

We know 70 tickets were sold, so:

 

A + K = 70.

 

We also know that $285 in ticket sales were sold. This tells us the cost of each ticket times the number of each ticket sold should total up to 285:

 

Ca*A + Ck*K = 285

4.50*A + 3.00*K = 285

 

Now we have two equations, two unknowns.

 

A + K = 70

4.50A + 3.00K = 285

 

Let's solve for K:

 

K = 70 - A

 

4.50A + 3.00(70-A) = 285

 

4.50A + 210 - 3.00A = 285

 

1.50A = 75

 

A = 50

 

K = 70 - 50 = 20

 

This means 50 adult tickets were sold and 20 kid tickets were sold. Let's check our work:

 

50*4.50 + 20*3.00 should be 285.

 

225 + 60 = 285. Check.

 

50 adult tickets + 20 kid tickets should be 70 total tickets.

 

50 + 20 = 70. Checkmate.

 

Hope this helps.