Tyler has some pennies and some nickels. he has no less than 15 coins worth at most
$0.55 combined. if tyler has 7 pennies, determine the maximum number of nickels
that he could have. if there are no possible solutions, submit an empty 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

4.6875 pounds

step-by-step explanation:

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