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Stacks of Coins
Dylan broke open his piggy bank and found a pile of quarters, dimes and pennies. He had a total of 52 coins. He used all of his coins
to buy a book for $5.98.
As he was stacking up his coins to pay the clerk, he realized 2 of the stacks had the same number of coins, while the 3rd stack had
twice as many coins. How many quarters, dimes and pennies did Dylan have?
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Respuesta :

SaniShahbaz

Answer:

26 Dimes, 13 Quarters and 13 Pennies = 13(0.10) + 13(0.25) + 26(0.01) = $ 5.98

Step-by-step explanation:

Worth of each of the coins is as follows:

Dime = $ 0.10

Quarter = $ 0.25

Penny = $ 0.01

Total worth of all the coins Dylan had is $ 5.98.

When Dylan made the stacks, there were same number of coins in 2 of the stacks and twice the number of coins in the 3rd stack.  Let n be the number of coins in each of the two stacks with same number of coins. So 2n will be the number of coins in 3rd stack. Since, Dylan had 52 coins in total, we can set up the equation as:

n + n + 2n = 52

4n = 52

n = 13

There are 13 coins in two stacks and 26 coins in 3rd stack. Based on this following are the 3 possibilities:

  • 13 Dimes, 13 Quarters and 26 Pennies
  • 13 Dimes, 26 Quarters and 13 Pennies
  • 26 Dimes, 13 Quarters and 13 Pennies

Value of the coins in total must be $ 5.98. Lets find the value of each of these combinations:

  • 13 Dimes, 13 Quarters and 26 Pennies = 13(0.10) + 13(0.25) + 26(0.01) = $ 4.81
  • 13 Dimes, 26 Quarters and 13 Pennies = 13(0.10) + 26(0.25) + 13(0.01) = $ 7.93
  • 26 Dimes, 13 Quarters and 13 Pennies = 13(0.10) + 13(0.25) + 26(0.01) = $ 5.98

Therefore, the correct combination of coins would be:

26 Dimes, 13 Quarters and 13 Pennies = 13(0.10) + 13(0.25) + 26(0.01) = $ 5.98

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