Total value of money

Question

A bank teller has a total of 70 bills in five ten and twenty dollar denominations. the total value of the money is $960. what are the total number of solutions? what is the solution with the smallest number of five-dollar bills? what is the solution with the largest number of five dollar bills?

Answer 1

x + y + z = 70'

5x +10t +20z = 960

infinite solutions without other restrictions

solution with 0 $5 bills is 26 $20's and 44 $10's

solution with largest number of $5's is 2 $10s, 40 $20s 28 $5s

x+z = 70

5x +20z = 960'

5x +5z = 350

15z = 610

z = 122/3 but can't have non integer bills

one solution for largest # of fives

2(10) + 40(20) + 28(5) = 20+820+140 = 960

2 +40 +28 = 70