Suppose there is a pile of quarters dimes and pennies with a total value of $1.07 how much of each coin can be present without being able to make change for a dollar? Of there are multiple selections of the coins that will work choose the selection with the largest total numbers of coins.

Verified Answer :

caylus

Hello,

Very nice as problem.

2 solutions:
1 quater,8 dimes, 2 pennies
and
3 quaters,3 dimes, 2 pennies

since
107=( 0, 0, 107) but : 100= 025+ 010+ 100
107=( 0, 1, 97) but : 100= 025+ 110+ 90
107=( 0, 2, 87) but : 100= 025+ 210+ 80
107=( 0, 3, 77) but : 100= 025+ 310+ 70
107=( 0, 4, 67) but : 100= 025+ 410+ 60
107=( 0, 5, 57) but : 100= 025+ 510+ 50
107=( 0, 6, 47) but : 100= 025+ 610+ 40
107=( 0, 7, 37) but : 100= 025+ 710+ 30
107=( 0, 8, 27) but : 100= 025+ 810+ 20
107=( 0, 9, 17) but : 100= 025+ 910+ 10
107=( 0, 10, 7) but : 100= 025+ 1010+ 0
107=( 1, 0, 82) but : 100= 125+ 010+ 75
107=( 1, 1, 72) but : 100= 125+ 110+ 65
107=( 1, 2, 62) but : 100= 125+ 210+ 55
107=( 1, 3, 52) but : 100= 125+ 310+ 45
107=( 1, 4, 42) but : 100= 125+ 410+ 35
107=( 1, 5, 32) but : 100= 125+ 510+ 25
107=( 1, 6, 22) but : 100= 125+ 610+ 15
107=( 1, 7, 12) but : 100= 125+ 710+ 5
107=( 1, 8, 2) is good
107=( 2, 0, 57) but : 100= 225+ 010+ 50
107=( 2, 1, 47) but : 100= 225+ 110+ 40
107=( 2, 2, 37) but : 100= 225+ 210+ 30
107=( 2, 3, 27) but : 100= 225+ 310+ 20
107=( 2, 4, 17) but : 100= 225+ 410+ 10
107=( 2, 5, 7) but : 100= 225+ 510+ 0
107=( 3, 0, 32) but : 100= 325+ 010+ 25
107=( 3, 1, 22) but : 100= 325+ 110+ 15
107=( 3, 2, 12) but : 100= 325+ 210+ 5
107=( 3, 3, 2) is good
107=( 4, 0, 7) but : 100= 425+ 010+ 0