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