place 20 pennies on the table in a row. Now replace every fourth coin wit a nickel. Now replace every third coin with a dime. Now repace every sixth coin with a quarter. What is the value of the 20 coins now on the table?
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I got $1.35
i got $1.53
my coins looked like
p p d n p q d n p p d q p p d n p q d n
8 pennies, 4 nickels, 5 dimes, 3 quarters
try again, because i do not guarantee that i did not make a mistake
20/4 = 5
5 of the pennies will be replaced by nickles
20/3 = 6.6 repeating, round down to 6
3 and 4 share the multiple 12, and 18, so two of your nickles are replaced with dimes
you now have 11 pennies, 3 nickles, and 6 dimes
20/6 = 3.3 repeating, round down to 3
3 and 6 share the multiples 6, 12, and 18
12 is a dime, and 18 is a dime
you have 11 pennies, 2 nickles, 4 dimes, and 3 quarters
\[(11*1) + (2*5) + (4+10) + (3*25) = $1.36\]
how can you have repeating decimal money?
you don't, you have uneven division which you round off; that's why I rounded all of the numbers down rather than to the nearest digit.
I rounded the number of coins, not the amount of money. :P
how can you have a fractional number of coins?
you replace every 6th coin with a quarter
20/6 = 3.333 coins replaced
you can only add 3 coins, because the fourth would land on 24, so you round it off.
i just got out some change and did it again
i got $1.30 this time
I'm gonna run the math one more time, 1 sec
i got $1.35 just like @Mindless143
coins # 4,8,16,20 are nickles
coins # 3,9,15 are dimes
coins # 6,12,18 are quarters
10 pennies, 4 nickles, 3 dimes, 3 quarters
\[10 + (4*5)+(3*10)+(3*25) = $1.35\]
so $1.35 was correct, I missed a coin or two apparently.