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?

ant101
Dec 29, 2017

#1**+1 **

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

CPhill
Dec 29, 2017