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?

Answer 1

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

Answer 2

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