A cash register contains 5 bills and 10 bills with a total v

A cash register contains $5 bills and $10 bills with a total value of $185. If there are 25 bills total, then how many of each does the register contain?

Solution

Let the number of $ 5 bills be x

and the number of $ 10 bills be y

the total value is $ 185

total value of $ 5 bills = 5 * number of bills(of $ 5)

                               = 5 *x = 5x

total value of $ 10 bills   = 10 * number of bills (of $ 10)                       

                                 = 10 *y = 10y

so the total value of these bills should be equal to $ 185

5x +10y = 185              (1)

total number of bills = 25

number of bills of $5 + number of bills of $ 10 = 25

x+y = 25              (2)

drom (1) and (2) we need to solve for x and y

(1) - 5*(2)                      // multiplying eq(2) by 5 and subtacting it from equation(1)

eq(2) * 5   => 5x + 5y = 125

5x +10y = 185

5x +5y = 125

-     -          -                        // subtarcting

we get

5y = 60

y = 12

from (2)

x + y = 25

x + 12 = 25

x = 13

so the number of bill of $ 5 = 13

number of bill of $ 10 = 12