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:
Q. 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:
Value Calculation: Understand the value of the coins and the total value needed.A nickel is worth $0.05 and a dime is worth $0.10. Lauren has 10 dimes, which are worth $1.00 in total (10 dimes * $0.10/dime).
Remaining Value: Calculate the remaining value needed to reach at least $1.35. Since Lauren already has $1.00 from the dimes, she needs at least $0.35 more ($1.35−$1.00).
Minimum Nickels Needed: Determine the minimum number of nickels needed to make up the remaining value.To make up at least $0.35 with nickels, Lauren would need a minimum of 7 nickels (since 7 nickels ∗$0.05/nickel=$0.35).
Total Number of Coins: Check if the total number of coins does not exceed 21. Lauren has 10 dimes and needs at least 7 nickels. The total number of coins would be 17 (10 dimes + 7 nickels), which does not exceed the maximum of 21 coins.
Solution Confirmation: Confirm that the solution meets all the given conditions.Lauren has 10 dimes worth $1.00 and at least 7 nickels worth $0.35, for a total of $1.35, which meets the condition of having no less than $1.35. The total number of coins is 17, which is no more than 21 coins.