At a local basketball game, all tickets are the
same price and all souvenirs are the same price.
mr. smith bought 2 tickets to this basketball game
and 1 souvenir for a total of $17.25. ms. lockhart
bought 5 tickets to the same game and 2 souvenirs
for a total of $42.00. how much was a ticket to
this game?

what is the answer?

Ticket cost of local basketball game is $7.50 and

Cost of souvenir is $2.50.

Solution:

First convert given statements into algebraic expression.

Let x be the cost price of local basketball game and y be the cost price of souvenirs.

Given Mr. Smith bought 2 basket ball game ticket and 1 souvenir for $17.25

⇒ 2x + y = 17.25

To equal this expression subtract 2x on both sides, we get

⇒         y = 17.25 – 2x – – – – (1)

Mr. Lockhart bought 5 basket ball game ticket and 2 souvenirs for $42.00

⇒ 5x + 2y = 42.00 – – – – (2)

Substitute equation (1) in equation (2)

⇒ 5x + 2(17.25 – 2x) = 42.00

⇒ 5x + 34.50 – 4x = 42.00

Combining like terms together.

⇒ 5x – 4x  = 42.00 – 34.50

⇒ x = 7.50

Now, substitute x = 7.50 in (1), we get

⇒ y = 17.25 – 2(7.50)

⇒ y = 17.50 – 15

⇒ y = 2.50

Hence, ticket cost of local basketball game is $7.50 and

cost of souvenir is $2.50.