Question

John has 76 marbles that are either blue, green, or red. He finds that there are more red marbles than green and 12 more green marbles than blue. How many red marbles does he have?

Answer 1

John's red marble count cannot be determined with the information given. We can infer that R > G and G = B + 12, but the exact count for each requires more specifics.

Step-by-step explanation:

To solve for the number of red marbles John has, we need to create a system of equations based on the information provided.

Let's use the following variables:

• 
  
• B for the number of blue marbles,
• 
  
• G for the number of green marbles, and
• 
  
• R for the number of red marbles.
• 
  

The problem states that:

1. 
   
3. John has a total of 76 marbles: B + G + R = 76,
4. 
   
6. There are more red marbles than green: R > G,
7. 
   
9. There are 12 more green marbles than blue: G = B + 12.
10. 
    

Now, let's substitute G from equation (3) into equation (1):

B + (B + 12) + R = 76

Combining like terms and simplifying, we get:

2B + R = 64

The problem doesn't give us enough information to find an exact number for each color, but we do know R must be larger than G, which is in turn 12 more than B. Therefore, the highest possible number for B would be if R and G were as close as possible in number, meaning just 1 more than G. If we set R to be G + 1, we could solve for B and G.

However, to fully solve the problem for R, additional information is necessary, such as the exact difference in number between R and G marbles.