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 ![p\leq 14](https://tex.z-dn.net/?f=p%5Cleq%2014)
According to their values.
⇒ ![0.05(n)+0.01(p)\leq \$\ 0.65](https://tex.z-dn.net/?f=0.05%28n%29%2B0.01%28p%29%5Cleq%20%5C%24%5C%200.65)
⇒ ![0.05(11)+0.01(p)\leq \$\ 0.65](https://tex.z-dn.net/?f=0.05%2811%29%2B0.01%28p%29%5Cleq%20%5C%24%5C%200.65)
⇒ ![\$\ 0.55+0.01(p)\leq \$\ 0.65](https://tex.z-dn.net/?f=%5C%24%5C%200.55%2B0.01%28p%29%5Cleq%20%5C%24%5C%200.65)
⇒ ![0.01(p)\leq \$\ 0.65-\$\ 0.55](https://tex.z-dn.net/?f=0.01%28p%29%5Cleq%20%5C%24%5C%200.65-%5C%24%5C%200.55)
⇒ ![0.01(p)\leq \$\ 0.10](https://tex.z-dn.net/?f=0.01%28p%29%5Cleq%20%5C%24%5C%200.10)
⇒ ![(p)\leq\frac{ \$\ 0.10}{0.01}](https://tex.z-dn.net/?f=%28p%29%5Cleq%5Cfrac%7B%20%5C%24%5C%200.10%7D%7B0.01%7D)
⇒
Minimum number of pennies :
⇒
which also satisfies
Therefore :
⇒
Plugging p= 10 we can verify the values.
⇒ ![0.05(11)+0.01(10)\leq \$\ 0.65](https://tex.z-dn.net/?f=0.05%2811%29%2B0.01%2810%29%5Cleq%20%5C%24%5C%200.65)
⇒ ![0.55+0.10\leq \$\ 0.65](https://tex.z-dn.net/?f=0.55%2B0.10%5Cleq%20%5C%24%5C%200.65)
⇒ ![\$\ 0.65\leq \$\ 0.65](https://tex.z-dn.net/?f=%5C%24%5C%200.65%5Cleq%20%5C%24%5C%200.65)
So,
Minimum number of pennies Hannah have = 10