In a basketball game, the Bulls scored a total of 103 points and made 3 times as many field goals (2 points each) as FREE throws (1 point each). They also made 11, 3-point baskets. How many field goals did they have?
$\displaystyle g$ stands for field goals scored in the game
$\displaystyle f$ stands for free throws scored in the game
$\displaystyle t$ stands for three-pointers scored in the game
So we know that: $\displaystyle 103=2g+f+3t$
We also know that: $\displaystyle g=3f$ and that: $\displaystyle t=11$
So substitute: $\displaystyle 103=2(3f)+f+3(11)$
Multiply: $\displaystyle 103=6f+f+33$
Therefore: $\displaystyle 70=7f$
So finally: $\displaystyle \boxed{f=10}$