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. $\newline$ Answer:

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Make predictions using experimental probability

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Q. 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.

\newline

Answer:

Calculate Total Value: First, let's calculate the total value of the $5$ nickels that Anna has. $\newline$ Since each nickel is worth $5$ cents, the value of $5$ nickels is $5$ nickels $\times$ $5$ cents/nickel.
Calculate Value of Nickels: Now, let's perform the calculation for the value of $5$ nickels. $\newline$ $5$ nickels $\times 5$ cents/nickel $= 25$ cents. $\newline$ So, Anna has $25$ cents from nickels.
Determine Additional Value: Next, we need to determine the minimum additional value Anna needs in dimes to reach at least $\$2$ . Since Anna already has $25$ cents from nickels, she needs at least $\$2 - 25$ cents in dimes.
Calculate Minimum Dimes Needed: Let's calculate the minimum additional value needed in dimes. $\$2$ - $25$ cents = $\$1.75$ or $175$ cents. Anna needs at least $175$ cents in dimes.
Find Minimum Number of Dimes: Each dime is worth $10$ cents. To find the minimum number of dimes needed to make $175$ cents, we divide $175$ cents by $10$ cents/dime.
Consider Maximum Number of Coins: Now, let's perform the division to find the minimum number of dimes. $\newline$ $175 \text{ cents} \div 10 \text{ cents/dime} = 17.5 \text{ dimes}$ . $\newline$ Since Anna cannot have half a dime, she needs at least $18$ dimes to reach the minimum value of $\$2$ .
Determine Range of Values: However, we must also consider the maximum number of coins Anna can have, which is $26$ coins in total. Since Anna already has $5$ nickels, she can have at most $26 - 5 = 21$ coins that are dimes.
Determine Range of Values: However, we must also consider the maximum number of coins Anna can have, which is $26$ coins in total. Since Anna already has $5$ nickels, she can have at most $26 - 5 = 21$ coins that are dimes.Finally, we determine the range of possible values for the number of dimes. Anna needs at least $18$ dimes to reach the minimum value of $\$$ $2$ , and she can have at most $21$ dimes based on the maximum number of coins she can have.
Determine Range of Values: However, we must also consider the maximum number of coins Anna can have, which is $26$ coins in total. $\newline$ Since Anna already has $5$ nickels, she can have at most $26 - 5 = 21$ coins that are dimes.Finally, we determine the range of possible values for the number of dimes. $\newline$ Anna needs at least $18$ dimes to reach the minimum value of $\$$ $2$ , and she can have at most $21$ dimes based on the maximum number of coins she can have.Therefore, the possible values for the number of dimes Anna could have are $18$ , $19$ , $20$ , and $21$ dimes.