If the total receipts were $1650, how many of each kind of ticket was sold?

Question

For the Athletic Banquet adult tickets cost $5.00 and student tickets cost $3.00. The committee sold twice as many student tickets as adult tickets. If the total receipts were $1650, how many of each kind of ticket was sold?

Answer 1

The best way to solve word problems is by first translating the words into Math.  Lets break this question down sentence by sentence.

1) "adult tickets cost $5.00 and student tickets cost $3.00" -  Let's say 'a' represents the number of adult tickets and 's' the number of student tickets sold.  

 

2) "The committee sold twice as many student tickets as adult tickets" - Since the number student tickets sold is twice as many as adult tickets, we can rewrite this in Math form as s=2a.  This is the first equation that we have.

 

3) "total receipts were $1650" -

Total receipts = (cost of adult ticket)(number of adult tickets sold) + (cost of student ticket)(number of student tickets sold)

$1650=($5)(a)+($3)(s)

1650=5a+3s and this is the second equation that we have to work with.

 

Whenever we have two variables (in this case, a and s) and two equations (in this case, s=2a and 1650=5a+3s), we can solve for the variables by substituting for one of variables into the other equation.  Since we know s=2a, we can plug for s in 1650=5a+3s.  So, we have:

1650=5a+3s

1650=5a+3(2a)

1650=5a+6a

1650=11a

Therefore, a=1650/11 which is a=150

Now, plugging in the value of a into the s=2a equation, we get,

s=2(150) and so s=300

 

Hope this helps!