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

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GCF and LCM: word problems

Full solution

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.

\newline

Answer:

Value Calculation: Understand the value of the coins and the total value needed. $\newline$ 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. $\newline$ 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. $\newline$ 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.

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