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

Question

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?

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Alexandra 2 weeks 2021-09-08T18:03:11+00:00 2 Answers 0

Answers ( )

    0
    2021-09-08T18:04:36+00:00

    Answer:

    8 red

    Step-by-step explanation:

    r/2 = y – 2 = ⅓ × o = (w+3)/3

    r + y + o + w = 35

    r = 8, y = 6, o = 12, w = 9

    0
    2021-09-08T18:05:05+00:00

    Answer:

    There are 8 red marbles

    Step-by-step explanation:

    Let the number of red be R , number of yellow be Y , number of orange be O and number of white be W. Then

    R+Y+O+W=35 ………………… *

    Half the number of red implies : \frac{R}{2}

    Two less than the number of yellow implies : y-2

    A third the number of orange implies : \frac{O}{2}

    A third of three more than the number of white marbles implies : \frac{1}{3}(W+3)

    combining everything together , we have

    \frac{R}{2}=Y-2=\frac{O}{2}=\frac{1}{3}(W+3)

    \frac{R}{2}=Y-2  implies : R = 2(Y-2)=2Y-4 ……………. equation 1

    Y-2=\frac{O}{2} implies : 2(Y-2) = O

    therefore: O = 2Y-4 …………………. equation 2

    Y-2 = \frac{1}{3}(W+3) implies : 3(Y-2)=W+3

    3Y-6=W+3

    Therefore: W=3Y-9 ……………………. equation 3

    Substituting equation 1 ,2 and 3 into equation * , we have

    2Y-4+Y+3Y-6+3Y-9=35

    9Y-19=35

    9Y=35+19

    9Y=54

    Y=54/9

    Y=6

    substitute the values of Y , to get R , O and W

    R=2Y-4

    R=2(6)-4

    R=12-4

    R=8

    O=3Y-6

    O=18-6

    O=12

    W=3Y-9

    W=18-9

    W=9

    Therefore:

    number of red = 8

    number of yellow = 6

    number of orange = 12

    number of white = 9

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