Question

There were 254 tickets purchased for a major league baseball game. The lower box tickets cost ​$12.50 and the upper box tickets cost ​$10.00. The total amount of money spent was ​$2745.00. How many of each kind of ticket were​ purchase

Answer 1

L = Lower box tickets amount.

U = Upper box tickets amount.

we know the whole amount sold were 254 of both, thus L + U = 254.

since we know the price of L is 12.5 for each, then the amount of money sold total for all of them has to be 12.5 * L, or 12.5L.

and the U is 10, so its total amount of money for it is 10U.

we also know that the total amount for both spent was 2745, thus 12.5L + 10U = 2745.

$\bf \begin{cases} L+U=254\implies \boxed{L}=254-U\\ 12.5L+10U=2745\\ ---------------\\ 12.5\left( \boxed{254-U} \right)+10U=2745 \end{cases} \\\\\\ 3175-12.5U+10U=2745\implies 3175-2.5U=2745 \\\\\\ 3175-2745=2.5U\implies 430=2.5U\implies \cfrac{430}{2.5}=U\implies 172=U$

so, 172 Upper box tickets were sold then.

how many Lower box tickets were sold?  well, L = 254 - U