Question

A cashier has 26 bills consisting of three times as many ones as fives, one less ten than fives, and the rest twenties. If the value is $120, find how many of each she has.

Answer 1

Let number of  fives = x then number of ones = 3x  and number of tens = x - 1

so we can create the equation 

x + 3x +  x-1 + y = 26  where y = number of twenties
so
5x + y = 27

also we have the equation 

5x + 3x + 10(x - 1) + 20y = 120

18x + 20y = 130..................................(1)
5x    + y    = 27     multiply  by -20:-
-100x - 20y = -540..............................(2)
Adding equation (1) and (2)
-82x = -410
x  = 5,  that is  5 fives

Now plug x = 5 into equation 1:-
18(5) + 20y = 130
20y =  40
y =  2 ,   that is 2 twenties

So the answer is   there are (3x) = 15 ones , 5  fives, 4 tens and 2 twenties