You have a collection of 50 marbles.

Question

You have a collection of 50 marbles. Each one is red, white, or green. You have twice as many red marbles as green marbles. The difference between the number of white marbles and the number of red marbles is four less than the nember of green marbles. How many marbles of each color do you have?

Answer 1

let G=# of green marbles

let 2G=# of red marbles

# of white minus number of red is 4 less than # of green

# of white-2G=G-4

# of white=2G+G-4

so we have:

G=# of green marbles

2G=# of red marbles

3G-4=# of white marbles

Only one variable !

G+2G+3G-4=50

6G-4=50

6G=54

G=9 green marbles

2G=18 red marbles

3G-4=27-4=23 white marbles

Answer 2

Hi Lexi;

You have a collection of 50 marbles. Each one is red, white, or green. You have twice as many red marbles as green marbles. The difference between the number of white marbles and the number of red marbles is four less than the nember of green marbles. How many marbles of each color do you have?

 

FIRST EQUATION...50=W+R+G

SECOND EQUATION...2G=R

THIRD EQUATION...G-4=W-R

 

Let's begin with the first equation...

50=W+R+G

Let's proceed with the third equation...

G-4=W-R

-4=W-R-G

Let's add the two equations together...

50=W+R+G

-4=W-R-G

46=2W+(0)R+(0)G

23=W

 

Let's return to the first equation...

50=W+R+G

50=23+R+G

Let's proceed with the second equation...

2G=R

Let's return to the first equation and substitute R with 2G...

50=23+2G+G

50=23+3G

27=3G

9=G

 

Let's return to the first equation...

50=W+R+G

50=23+R+9

50=32+R

18=R

 

Let's return to the first equation...

50=W+R+G

50=23+18+9

50=50

 

Let's return to the second equation...

2G=R

(2)(9)=18

18=18

 

Let's return to the third equation...

G-4=W-R

9-4=23-18

5=5

Answer 3

Define your variables:

R = NUMBER RED MARBLES

W= NUMBER WHITE MARBLES

G = NUMBER GREEN MARBLES

 

Now get your equations: You will have three since there are three unknowns

 

(1) R+W+G=50

(2) 2R=G

(3) W-R=G-4

 

The objective is to plug in one equation into another to get all one type of unknown.  

Plug 2 into 3 to get  (4) W-R=2R-4.  

Plug 2 into 1 to get  (5) 3R+W=50

Solve (4) for R to get W=3R-4

Now plug it into (5) to get 6R-4=50. Now R=9

Use this to plug into (2) to get G=18

Use those two to plug into (1) to get 27+W=50. So W=23.

 

Your final answer: 9 Red marbles, 18 green marbles, and 23 white marbles.