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

8 red

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

There are 8 red marbles

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 :
`(R)/(2)`

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

A third the number of orange implies :
`(O)/(2)`

A third of three more than the number of white marbles implies :
`(1)/(3)(W+3)`

combining everything together , we have

`(R)/(2)=Y-2=(O)/(2)=(1)/(3)(W+3)`

`(R)/(2)=Y-2` implies :
`R = 2(Y-2)=2Y-4` ................ equation 1

`Y-2=(O)/(2)` implies :
`2(Y-2) = O`

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

`Y-2 = (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