Question

a bag holds 1200 marbles colored either blue, red, green, or pink. there are 2 more blue than green, 6 more green than red and 6 more red than pink. how many marbles are blue?

Answer 1

b = 2 + g . . . (1)
g = 6 + r . . . (2)
r = 6 + p . . . (3)

Putting (3) into (2) gives:
g = 6 + 6 + p = 12 + p . . . (4)
Putting (4) into (1) gives:
b = 2 + 12 + p = 14 + p . . . (5)

b + g + r + p = 1200
2 + g + 6 + r + 6 + p + p = 1200
2 + 12 + p + 6 + 6 + p + 6 + p + p = 1200
32 + 4p = 1200
4p = 1200 - 32 = 1168
p = 292

From (5), b = 14 + p = 14 + 292 = 306

Therefore, there are 306 blue mables.