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Lauren has some nickels and some dimes. She has no more than 21 coins worth no less than 
$1.35 combined. If Lauren has 10 dimes, determine the minimum number of nickels that she could have.
Answer:

Lauren has some nickels and some dimes. She has no more than 2121 coins worth no less than $1.35 \$ 1.35 combined. If Lauren has 1010 dimes, determine the minimum number of nickels that she could have.\newlineAnswer:

Full solution

Q. Lauren has some nickels and some dimes. She has no more than 2121 coins worth no less than $1.35 \$ 1.35 combined. If Lauren has 1010 dimes, determine the minimum number of nickels that she could have.\newlineAnswer:
  1. Value Calculation: Understand the value of the coins and the total value needed.\newlineA nickel is worth $0.05\$0.05 and a dime is worth $0.10\$0.10. Lauren has 1010 dimes, which are worth $1.00\$1.00 in total (1010 dimes * $0.10\$0.10/dime).
  2. Remaining Value: Calculate the remaining value needed to reach at least $1.35\$1.35. Since Lauren already has $1.00\$1.00 from the dimes, she needs at least $0.35\$0.35 more ($1.35$1.00\$1.35 - \$1.00).
  3. Minimum Nickels Needed: Determine the minimum number of nickels needed to make up the remaining value.\newlineTo make up at least $0.35\$0.35 with nickels, Lauren would need a minimum of 77 nickels (since 77 nickels * $0.05/nickel=$0.35\$0.05/nickel = \$0.35).
  4. Total Number of Coins: Check if the total number of coins does not exceed 2121. Lauren has 1010 dimes and needs at least 77 nickels. The total number of coins would be 1717 (1010 dimes + 77 nickels), which does not exceed the maximum of 2121 coins.
  5. Solution Confirmation: Confirm that the solution meets all the given conditions.\newlineLauren has 1010 dimes worth $1.00\$1.00 and at least 77 nickels worth $0.35\$0.35, for a total of $1.35\$1.35, which meets the condition of having no less than $1.35\$1.35. The total number of coins is 1717, which is no more than 2121 coins.

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