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Leah has some pennies and some nickels. She has a maximum of 2121 coins worth a minimum of $0.57\$0.57 combined. If Leah has 99 pennies, determine all possible values for the number of nickels that she could have.

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Full solution

Q. Leah has some pennies and some nickels. She has a maximum of 2121 coins worth a minimum of $0.57\$0.57 combined. If Leah has 99 pennies, determine all possible values for the number of nickels that she could have.
  1. Calculate Pennies Value: Leah has 99 pennies, which is $0.09\$0.09. To find out the minimum number of nickels, subtract the value of the pennies from the total value.\newline$0.57−$0.09=$0.48\$0.57 - \$0.09 = \$0.48
  2. Find Minimum Number of Nickels: Each nickel is worth \$\(0\).\(05\). Divide the remaining value by the value of one nickel to find the minimum number of nickels.\(\newline\)\(\$0.48 \div \$0.05 = 9.6\)\(\newline\)Since Leah can't have a fraction of a coin, she needs at least \(10\) nickels.
  3. Find Maximum Number of Nickels: Now, let's find the maximum number of nickels. Leah has a maximum of \(21\) coins, and she already has \(9\) pennies.\(\newline\)\(21 - 9 = 12\)\(\newline\)Leah could have up to \(12\) nickels.
  4. Final Number of Nickels: So, Leah could have between \(10\) and \(12\) nickels.

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