A Starbucks on campus sells cappuccinos in three sizes: tall for $2.65, grande for $3.20, and venti for $3.50. One morning, Brianna served 50 cappuccinos. The number of tall and venti cappuccinos, combined, was 2 fewer than the number of grande cappuccinos. If she collected a total of $157, how many cappuccinos of each size were sold?

t+g+v = 50

t+v = g-2
2.65t + 3.20g + 3.50v = 157.00

t=12
g=26
v=12