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

Minimum number of pennies = 10

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( \$\ 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