Last week, the number of type B cabinets produced was 30 more than 1/2 the number of type A cabinets produced. The number of type C cabinets produced was 20 more than 3/2 times the number of type A cabinets produced.

B = 1/2A + 30

C = 3/2A + 20

B = C

1/2A + 30 = 3/2A + 20

30 - 20 = 3/2A - 1/2A

10 = A < = = = there were 10 type A cabinets produced

B = 1/2A + 30

B = 1/2 (10) + 30

B = 5 + 30

B = 35 ... there were 35 type B cabinets produced

B = C ... so there was 35 type C cabinets produced

for a total of : (10 + 35 + 35) = 80 cabinets produced <===