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there are 84 quarters lined up. You start at the beginning, replacing every 2nd coin with a dime. Then you go to the beginning of the line and replace every third coin with a nickel. Then you start at the beginning and replace every fourth coin with a penny. How much is this row of coins worth in cents?

Guest Dec 10, 2014

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 #3
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You guys are awesome! Thank you so much, it helped a lot. I appreciate it!

Guest Dec 17, 2014
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 #1
avatar+17711 
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Let's see:  you start with 84 quarters.

Now you change every 2nd quarter with a dime; so you now have 42 quarters (those in odd-numbered locations) and 42 dimes (those in even numbered locations).

When you change every third coin with a nickel, half of them will come from odd-numbered locations and half will come from even-numbered locations. Since 84 divided by 3 is 28, 14 nickels will be in odd-numbered locations and 14 will be in even numbered locations. You now have 28 quarters and 14 nickels in odd-numbered locations and 28 dimes and 14 nickels in even-numbered locations.

Changing every fourth coin with a penny, will place 21 pennies, all in even-numbered locations; 14 in locations that have dimes and 7 in locations that have nickels.

In odd-numbered locations, you have 28 quarters and 14 nickels; in even-numbered locations, you have 14 dimes, 14 pennies, 7 nickels and 7 pennies.

Total:  28 quarters, 14 dimes, 21 nickels, and 21 pennies

geno3141  Dec 11, 2014
 #2
avatar+81032 
+5

All we really need to do is to look at the first 12 coins..(the common denominator of 2, 3 and 4)....whatever pattern that exists there just repeats itself 7 times

We will have

Q D N P Q N Q P N D Q P

So we have

4 x 7 = 28 quarters

2 x 7 = 14 dimes

3 x 7 = 21 nickels and 21 pennies

The same as geno found....

I'll let you total the money....!!!!  (in pennies, remember !!!)

 

CPhill  Dec 11, 2014
 #3
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Best Answer

You guys are awesome! Thank you so much, it helped a lot. I appreciate it!

Guest Dec 17, 2014

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