Question

i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)

Answer 1

We know that the total number of coins is 17.

N of the coins are nickels, and the rest of the coins are dimes.

Then the number of dimes is given by the difference between the total number of coins and the number of nickels, thus, there are:

17 - N dimes.

Each nickel has a value of $0.05

each dime has a value of $0.10

Then if you have N nickels and (17 - N) dimes, the total amount of money that you have is:

$0.05*N + (17 - N)*$0.10

This is the first expression, the second one comes if we simplify this.

First, we expand the second term:

$0.05*N + 17*$0.10 - N*$0.10

Now we can take the common factor N to get:

N*($0.05 - $0.10) + $1.70 = $1.70 - $0.05*N

$1.70 - $0.05*N is the simplified expression.