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Anna has some nickels and some dimes. She has at most 26 coins worth a minimum of $2 combined. If Anna has 5 nickels, determine all possible values for the number of dimes that she could have. Answer:

Anna has some nickels and some dimes. She has at most 2626 coins worth a minimum of $2\$2 combined. If Anna has 55 nickels, determine all possible values for the number of dimes that she could have.\newlineAnswer:

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Q. Anna has some nickels and some dimes. She has at most 2626 coins worth a minimum of $2\$2 combined. If Anna has 55 nickels, determine all possible values for the number of dimes that she could have.\newlineAnswer:
  1. Calculate Total Value: First, let's calculate the total value of the 55 nickels that Anna has.\newlineSince each nickel is worth 55 cents, the value of 55 nickels is 55 nickels ×\times 55 cents/nickel.
  2. Calculate Value of Nickels: Now, let's perform the calculation for the value of 55 nickels.\newline55 nickels ×5\times 5 cents/nickel =25= 25 cents.\newlineSo, Anna has 2525 cents from nickels.
  3. Determine Additional Value: Next, we need to determine the minimum additional value Anna needs in dimes to reach at least $2\$2. Since Anna already has 2525 cents from nickels, she needs at least $2−25\$2 - 25 cents in dimes.
  4. Calculate Minimum Dimes Needed: Let's calculate the minimum additional value needed in dimes.$2\$2 - 2525 cents = $1.75\$1.75 or 175175 cents. Anna needs at least 175175 cents in dimes.
  5. Find Minimum Number of Dimes: Each dime is worth 1010 cents. To find the minimum number of dimes needed to make 175175 cents, we divide 175175 cents by 1010 cents/dime.
  6. Consider Maximum Number of Coins: Now, let's perform the division to find the minimum number of dimes. \newline175 cents÷10 cents/dime=17.5 dimes175 \text{ cents} \div 10 \text{ cents/dime} = 17.5 \text{ dimes}.\newlineSince Anna cannot have half a dime, she needs at least 1818 dimes to reach the minimum value of $2\$2.
  7. Determine Range of Values: However, we must also consider the maximum number of coins Anna can have, which is 2626 coins in total. Since Anna already has 55 nickels, she can have at most 26−5=2126 - 5 = 21 coins that are dimes.
  8. Determine Range of Values: However, we must also consider the maximum number of coins Anna can have, which is 2626 coins in total. Since Anna already has 55 nickels, she can have at most 26−5=2126 - 5 = 21 coins that are dimes.Finally, we determine the range of possible values for the number of dimes. Anna needs at least 1818 dimes to reach the minimum value of $\$22, and she can have at most 2121 dimes based on the maximum number of coins she can have.
  9. Determine Range of Values: However, we must also consider the maximum number of coins Anna can have, which is 2626 coins in total.\newlineSince Anna already has 55 nickels, she can have at most 26−5=2126 - 5 = 21 coins that are dimes.Finally, we determine the range of possible values for the number of dimes.\newlineAnna needs at least 1818 dimes to reach the minimum value of $\$22, and she can have at most 2121 dimes based on the maximum number of coins she can have.Therefore, the possible values for the number of dimes Anna could have are 1818, 1919, 2020, and 2121 dimes.

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