Question

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.

Answer 1

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.

⇒ $n+p\leq 25$  and $11+p\leq 25$ so $p\leq 14$

According to their values.

⇒ $0.05(n)+0.01(p)\leq \ \ 0.65$

⇒ $0.05(11)+0.01(p)\leq \ \ 0.65$

⇒ $\ \ 0.55+0.01(p)\leq \ \ 0.65$

⇒ $0.01(p)\leq \ \ 0.65-\ \ 0.55$

⇒ $0.01(p)\leq \ \ 0.10$

⇒ $(p)\leq\frac{ \ \ 0.10}{0.01}$

⇒ $(p)\leq 10$

Minimum number of pennies :

⇒ $(p)\leq 10$ which also satisfies $p\leq 14$

Therefore :

⇒ $p=10$

Plugging p= 10 we can verify the values.

⇒ $0.05(11)+0.01(10)\leq \ \ 0.65$

⇒ $0.55+0.10\leq \ \ 0.65$

⇒ $\ \ 0.65\leq \ \ 0.65$

So,

Minimum number of pennies Hannah have = 10