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My name is Ann [436]
2 years ago
8

There are thirty-five red, yellow, orange, and white marbles in a bag. If half the number of red marbles equals two less than th

e 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?
Mathematics
2 answers:
Effectus [21]2 years ago
4 0

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

MArishka [77]2 years ago
3 0

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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