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A jar contains n nickels and d dimes. There is a total of 236 coins in the jar. The value of the coins is $15.75. How many nickels and how many dimes are in the jar

User Shuo
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1 Answer

5 votes

The total if all 236 coins were nickels would be $11.80, which is $3.95 short of the actual amount.

Replacing a nickel with a dime adds $0.05 to the total value, so there must have been $3.95/$0.05 = 79 such replacements.

There are 79 dimes.

There are 236 -79 = 157 nickels.

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Using the given variables, the problem statement gives rise to two equations. One is the based on the number of coins. The other is based on their value.

  • n + d = 236
  • .05n +.10d = 15.75

Solving the first for n, we get

... n = 236 - d

Substituting that into the second equation, we have

... .05(236 -d) +.10d = 15.75

... .05d = 15.75 -236·.05 . . . . . collect terms, subtract .05·236

... d = 3.95/.05 . . . . . . . . . . . . . divide by .05

... d = 79

... n = 236-79 = 157

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The solution should look familiar, as it matches the verbal description at the beginning.

User Prasad Revanaki
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