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# Thehe number of orange marbles, and equals a third of three more than the number of white marbles, how many red marbles are there?

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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
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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

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