can you help with a system of equations word problem?

Question

You have decided to give your best friend a bag of red and green marbles for his birthday.  Your friend likes green marbles better than red ones, so the bag has twice as many green marbles as red.  The label on the bag says it contains a total of 84 marbles.  How many green marbles are in the bag?  Write a system of equations for this problem.  Then solve the problem using any method you like.  Be sure to check your solution.

Answer 1

Hi Logan.

 

If R = the number of red marbles and

   G = the number of green marbles,

then you can represent this situation as

 

R + G = 84    (the bag has only red and green marbles, and there are 84 total marbles)

 

and

 

G = 2R    (tempting to write it the other way, but this way there are more green marbles like we wanted)

 

 

Substitute G = 2R into the first equation

 

R + 2R = 84

 

Combine like terms

 

3R = 84

 

Divide both sides by 3

 

R = 28 

 

G = 2 R = 2 (28) = 56

 

So there are 28 red marbles and 56 green marbles.