Help!!! Word problems using systems of equations?

Question

Irene has $4.50 in her coin bank in nickles and dimes. The number of dimes is twice the number of nickles. How many coins of each type does irene have?

Answer 1

Put each sentence in the form of an equation:

Let N be the number of nickels and D be the number of dimes.

We know that 5 cents per nickel times the number of nickels, plus ten cents per dime times the number of dimes, equals a total of four dollars and fifty cents. If you don't actually have to SOLVE this word problem but simply express it as a system of equations, you can write this first equation as:

$0.05 * N + $0.10 * D = $4.50

But if you are actually going to solve it, express it in cents rather than dollars to save yourself the trouble of dealing with decimal points:

5N + 10D = 450

We also know that there are twice as many dimes as nickels, a fact that we can express using a second equation:

D = 2N

To actually solve the word problem to determine the number of nickels and dimes, we would then substitute "2N" for "D" in the first equation:

5N + 10(2N) = 450
5N + 20N = 450
25N = 450
N = 450/25
N = 18

Irene has 18 nickels in the piggybank.

Now we put that back into the second equation to solve for the number of dimes:

D = 2N
D = 2 * 18
D = 36

Irene has 36 dimes in her piggybank.

Now, double-check the answer by checking the results:

Does 18 nickels plus 36 dimes equal $4.50?
Does $0.90 + $3.60 = $4.50?
Does $4.50 = $4.50? *** YES ***

Since the answers check out, we have the solution.

Answer 2

let d=# of domes & n=# of nickles:
10d+5n=450
d=2n
10*2n+5n-450
20n + 5n=450
25n=450
n=18
d=2n=2*18=36
check:
10*36+5*18=360+90=450 cents=$4.50
18 nickles
36 dimes

Answer 3

so
d = 2n
d + 5n = 450 (i multiplied this by 100 jsut to make it easier, divide at end)

so 2n + 5n = 450
7n = 450
But you must've written the problem wrong.. cos it should be a whole number so check to make sure you wrote it right?

Answer 4

problem is messed up...you cant have half a dime