+885 There are thirty-five red, yellow, orange, and white marbles in a bag. If half the number of red marbles equals two less than the number of yellow marbles, equals a third the number of orange marbles, and equals a third of three more than the number of white marbles, how many red marbles are there?
+129852 R + Y + O + W = 35
R/2 = Y - 2 ⇒ Y = R/2 + 2 (1)
R/2 = O/3 ⇒ O = (3/2)R (2)
R/2 = (W + 3) / 3 ⇒ (3/2)R = W + 3 ⇒ (3/2)R - 3 = W (3)
Sub (1), (2), (3) into the first equation
R + R/2 + 2 + (3/2)R + (3/2)R - 3 = 35
4R + R/2 = 36
8R + R = 72
9R = 72
R = 8 = red marbles
And
Y = 8/2 + 2 = 6
O = (3/2)8 = 12
W = (3/2)(8) - 3 = 9
