Math story problem that has me at a loss as to where to start?

Question

If you could just give me a starting point then I should be able to solve the problem ... I just have no idea how to set up the equation/s.

Thanks for any help and understanding I just want a little help not the answer!

Jamil always throws loose change into a pencil holder on his desk and takes it out every
two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as
nickels, and the value of the dimes is $5.10 more than the value of the nickels. How many
nickels and dimes does Jamil have?

Answer 1

D = 9N
10D = 5N + 510

Solve by substitution: 10*9N = 5N + 510, etc...

Answer 2

OK, off the top of my head, I'd say you'll want to start by representing the number of nickels as N, and the number of dimes as D. Then use the information given to you: there are 9 times as many dimes as nickels, OK, D = 9N. What about the second thing? What's the "value" of one dime? Well, ten cents, or 0.1. The value of 2 dimes is 0.2, of 3 is 0.3, etc. In other words, to get the value of D dimes, you multiply D by 0.1. So the value of the dimes, 0.1D, is 5.10 more than the value of the nickels, which is 0.05N. So

0.1D = 5.10 + 0.05N
And we already established that
D = 9N

Now substitute the bottom one into the top one, and you've got your answer!

Answer 3

In order to start, you need to setup a system of equations.
Since we know that there are 9 times as many dimes (d) than nickels (n), we can write the relationship:
d = 9n (9 dimes for every nickel there is).

Also, since the dimes are worth 10 cents and the value of the dimes 5.10 more than that of the nickels, we can write:
.1d = .05n + 5.1

Since d = 9n, we plug that into the n variable in the second equation.
.1(9n) = .05n +5.1

Solve for d:
.9n = .05n + 5.1
.85n = 5.1
n = 6
Plugging into the first equation, d= 9 x 6 = 54.

Answer 4

You can work this out all in dollars or all in cents. Cents is easier because you can use integers.

Let
n = number of nickels
d = number of dimes

Given
d = 9n
10d = 5n + 510

Substitute d from the first equation into the second.

10d = 5n + 510
10(9n) = 5n + 510
90n = 5n + 510
85n = 510
n = 6

d = 9n = 9*6 = 54

There are 6 nickels and 54 dimes.

Answer 5

You have n nickels and d dimes.

There are 9 times as many dimes as nickels:
d=9n

The value of the dimes is $5.10 more than the value of the nickels:

.1d = .05n + 5.1

Now solve for d and n.

Answer 6

count: d = 9n
value: 10d = 510 + 5n

replace d with 9n

10(9n) = 510 + 5n
90n = 510 + 5n
85n = 510
n = 6
d = 54

Answer 7

Let x = number of nickles
Then 9x = number of dimes.
So 0.05x +0.1(9x) = 5.1 is your equation.