Respuesta :
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.
⇒ [tex]n+p\leq 25[/tex] and [tex]11+p\leq 25[/tex] so [tex]p\leq 14[/tex]
According to their values.
⇒ [tex]0.05(n)+0.01(p)\leq \$\ 0.65[/tex]
⇒ [tex]0.05(11)+0.01(p)\leq \$\ 0.65[/tex]
⇒ [tex]\$\ 0.55+0.01(p)\leq \$\ 0.65[/tex]
⇒ [tex]0.01(p)\leq \$\ 0.65-\$\ 0.55[/tex]
⇒ [tex]0.01(p)\leq \$\ 0.10[/tex]
⇒ [tex](p)\leq\frac{ \$\ 0.10}{0.01}[/tex]
⇒ [tex](p)\leq 10[/tex]
Minimum number of pennies :
⇒ [tex](p)\leq 10[/tex] which also satisfies [tex]p\leq 14[/tex]
Therefore :
⇒ [tex]p=10[/tex]
Plugging p= 10 we can verify the values.
⇒ [tex]0.05(11)+0.01(10)\leq \$\ 0.65[/tex]
⇒ [tex]0.55+0.10\leq \$\ 0.65[/tex]
⇒ [tex]\$\ 0.65\leq \$\ 0.65[/tex]
So,
Minimum number of pennies Hannah have = 10
