How many tickets were sold?

Question

There were 345 tickets purchased for a major league baseball game. The lower reserved tickets cost

​$9.50 and the upper reserved tickets cost ​$8.00 The total amount of money spent was $2809.50

How many of each kind of ticket were​ purchased?

Answer 1

Let x be the number of lower reserved tickets.

Then the number of upper reserved tickets is 345 – x.

The revenue from lower reserved tickets is x · $9.50.

The revenue from upper reserved tickets is (345 – x) · $8.00

The total revenue is therefore x · $9.50 + (345 – x) · $8.00.

So we have (x · $9.50) + (345 – x) · $8.00 = $2809.50.

This simplifies to $1.50 x + $2760 = $2809.50.

Subtracting $2760 from both sides, we get $1.50 x = $49.50.

Then dividing each side by $1.50, we get 33.

Thus there were 33 lower reserved tickes and 312 upper reserved tickets.

You can check that by arithmetic, thus:

(33 · $9.50) + (312 · $8.00) = $2809.50.