Hannah has some pennies and some nickels. She has a maximum of 25 coins worth a minimum of $0.65 combined. If Hannah has 11 nickels, determine the minimum number of pennies that she could have. If there are no possible solutions, submit an empty answer.

Minimum number of pennies = 10

Step-by-step explanation:

Given:

Maximum number of coins Hannah have = 25

Total number of of nickels (coins) she has = 11

Total value of the combined coins = $ 0.65

We have to find the minimum number of pennies.

Let the number of pennies be "p"  and no. of nickels be "n".

Note:

Value of 1 penny = $ 0.01

Value of 1 nickel = $ 0.05

Arranging the above situation in terms of equations:

According to their quantities.

⇒  and so

According to their values.

⇒

⇒

⇒

⇒

⇒

⇒

⇒

Minimum number of pennies :

⇒ which also satisfies

Therefore :

⇒

Plugging p= 10 we can verify the values.

⇒

⇒

⇒

So,

Minimum number of pennies Hannah have = 10

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step-by-step explanation:

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