SOLUTION: Prove that a cashier with only dimes and quarters can make change for any multiple of 5 cents that is 20 cents or greater. PROVE BY BASIC AND INDUCTIVE STEP

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Question 846562: Prove that a cashier with only dimes and quarters can make
change for any multiple of 5 cents that is 20 cents or greater.
PROVE BY BASIC AND INDUCTIVE STEP
Found 2 solutions by richwmiller, richard1234:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2*10=20
25=25
3*10=30
10+25=35
4*10=40
25+20=45
25+25=50
25+30=55
50+10=60
25+40=65
50+20=70
3*25=75
50+30=80
75+10=85
50+40=90
75+20=95
4*25=100









Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Base case: 20 cents is doable with 2 dimes.

Assume 5k cents is doable where k >= 4. To make 5k+5 cents we can either replace two dimes with a quarter, or replace a quarter with three dimes. Since we must have either two dimes or a quarter (or both), one of the scenarios is possible, and hence we can make 5k+5 cents.