The basketball team sell t-shirts and hats as a fundraiser. they sold a total of 23 items and made a profit of $246. they made a profit of $10 for every t-shirt they sold and $12 for every hat they sold.

S - the number of the t-shirts;
h - the number of hats:
The system of equations:
s + h = 23
10 s + 12 h = 246

s = 23 - h
10 * ( 23 - h ) + 12 h = 246
230 - 10 h + 12 h = 246
2 h = 246 - 230
2 h = 16
h = 16 : 2
h = 8
s = 23 - 8
s = 15
The basketball team sold 15 t-shirts and 8 hats.