Question 288580: how many different combinations of stamps can you use for an exact postage on a package that requires $4.95 of stamps if you only have $0.45 and $0.20 stamps ?
a 1 b 2 c 3 d 4 e 5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4.95 / .45 = 11.
4.95 / .20 = 24.
You can have 11 * 45 cent stamps because 45 cents divides evenly into $4.95.
If you drop one 45 cent stamp then two twenty cent stamps will be a nickel shy.
If you drop two 45 cent stamps, then four 20 cent stamps will be a dime shy.
If you drop three 45 cent stamps, then six 20 cent stamps will be 15 cents shy.
If you drop four 45 cent stamps, then eight 20 cent stamps will be 20 cents shy, but you can then add one 20 cent stamp to make up the difference.
your combinations so far are:
Eleven 45 cent stamps for a total of $4.95
Seven 45 cent stamps plus nine 20 cent stamps for a total of $3.15 plus $1.80 = $4.95.
Drop another four 45 cent stamps and add another nine 20 cent stamps to get:
Three 45 cent stamps plus eighteen 20 cent stamps for a total of $1.35 + $3.60 = $4.95.
So far you have a total of three possible combinations.
I don't think there's any more.
Your answer should be selection c (3).
I'll work my way back up and see if there's any more.
You start with $4.95
You can't do it with all 20 cent stamps because $4.95 / .2 is not an integer.
Subtract one 45 cent stamp to get $4.50 / .2 is not an integer.
Subtract two 45 cent stamps to get $4.05 / .2 is not an integer.
Subtract three 45 cent stamps to get $3.60 / .2 IS AN INTEGER !!!!!.
Subtract four 45 cent stamps to get $3.15 / .2 is not an integer.
Subtract five 45 cent stamps to get $2.70 / .2 is not an integer.
Subtract six 45 cent stamps to get $2.25 / .2 is not an integer.
Subtract seven 45 cent stamps to get $1.80 / .2 IS AN INTEGER !!!!!.
Subtract eight 45 cent stamps to get $1.35 / .2 is not an integer.
Subtract nine 45 cent stamps to get $.90 / .2 is not an integer.
Subtract ten 45 cent stamps to get $.45 / .2 is not an integer.
Subtract Eleven 45 cent stamps to get $0.0 / .2 IS AN INTEGER !!!!!.
There are only 3 possible combinations.
Your answer is confirmed.
That answer is selection c (3).
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