Explain why 1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar

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21-08-2016
Mathematics

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Explain why 1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar

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caylus caylus · Answer 1 · 2016-08-21T14:26:42+02:00

caylus caylus

21-08-2016

Hello,

There are only 2 solutions for $1.19

In cents:
119=1*25+9*10+0*5+4*1
119=3*25+4*10+0*5+4*1

Thus
120=119+1=(1*25+9*10+0*5+4*1) +1 =1*25+9*10+0*5+5*1
but 1*25+7*10+0*5+5*1=100

120=119+1=(3*25+4*10+0*5+4*1)+1=3*25+4*10+0*5+5*1
but 3*25+2*10+0*5+5*1=100

So there are no solution for $1.20

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