Question

1000 tickets were sold. Adult tickets cost $4.50, children's cost $2.50, and a total of $5300 was collected. How many tickets of each kind were sold

this is algebra question

Answer 1

Let the number fo Adult tickets sold be A and children tickets sold be C

we have,

A + C = 1000.................................(1)

4.5A + 2.5C = 5300.......................(2)

(2) - 2.5*(1)

=> 4.5A + 2.5C - 2.5A - 2.5C = 5300 - 2500

=> 2A = 2800

=> A = 1400

Putting the value A=1400 in (1) we get,

1400 + C = 1000

=> C = -400

The number of tickets sold can not ofcourse be negative and this leads to a contradiction in the question itslef.

We can see that the maximum tickets sold are 1000. Even if all the tickets are sold in the higehr price adult category, the maximum revenue that cna be geenrated is 1000*4.5 = 4500

Revenue of 5300 can never be generated by selling 1000 tickets at the given price.

Thus, there are no values of tickets sold to adults and children that satisfy the criteria