Answer: He only can have 9 nickels.
Step-by-step explanation:
Let's define P as the number of pennies and N as the number of nickels.
P + N > 15
because he has no less than 15 coins in total.
and:
P*$0.01 + N*$0.05 ≥ $0.55
Because he has at most, $0.55
Now, if P = 7
Now we need to solve:
7*$0.01 + N*$0.05 ≥ $0.55
N*$0.05 ≥ $0.55 - $0.07 = $0.48
Now, with the equality of this relation, we can find the maximal value of N.
N*$0.05 = $0.48
N = 0.48/0.05 = 9.6
So the maximum number of nickels he can have is 9.6, but he can not have a 0.6 of a nickel, so we need to round down to 9.
Now, we also know that he no less than 15 coins in total, with that equation we can find the minimal value of N.
7 + N > 15.
N > 15 - 7 = 8
So we have the range:
8 < N ≤ 9
This means that the only possible value of N is 9
