A student has some 1 bills and $5 bills in his wallet. he has a total of 15 bills that are worth $47. how many of each type of bill does he have?

*Given
Total number of bills    - 15
Total value of the bills - $47
Bills                             - $1 and $5

*Solution
Let:
  x - number of $1 bills
  y - number of $5 bills

1. The total number of bills comprising of $1 and $5 bills is 15. Thus, 

                         x + y = 15                                      (EQUATION 1)

2. The total value of the bills is $47. Thus, 
 
                   $1 (x) + $5 (y) = $47                           (EQUATION 2)

3. There are 2 ways to solve this (system of linear equations) mathematically. You can use the elimination method or the substitution method. Using the elimination method to eliminate the variable x... (subtract Equation 1 from Equation 2)

                    1x      +   5y      = 47
                 _
                     x       +     y      = 15
                     0       +   4y      = 32

4. Thus, the value of y, which is the number of $5 bills is, 

                     4y       =   32 
                      4              4

                      y       =    8

5. The number of $1 bills (x) can then be solved using either Equations 1 or         2. Using Equation 1 to determine x, 
 
                         x + y = 15    
                               x = 15 - y
                               x = 15 - 8
                               x = 7

From the solution, we have determined that there are 8 pieces of $5 bills and 7 pieces of $1 bills.