If 12a+3b=1 and 7b–2a=0, what is the average of a and b?

The mean/average of a and b is 1/20.

Step-by-step explanation:

Recall that the average of two numbers is equal to the sum of the numbers divided by 2.  Thus, we need to find (a+b)/2.

We'll first solve the system

12a+3b=1

7b–2a=0

I used matrices to solve this system:  a=7/90 and b = 1/45.

Another possible approach would be to use elimination by  addition and subtraction to solve this system.  Do 7/90 and 1/45 satisfy 7b-2a=0?  Yes.  Do 7/90 and 1/45 satisfy 12a+3b=1?  Yes.

Now we need to find (a+b)/2:  

7/90 + 1/45          7/90 + 2/90         9/90

= = = 1/20

      2                             2                      2

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw