Solve Algebraically

1) Rachel paid $1.45 for postage with nickels and dimes. She gave to postal clerk 7 more more than dimes than nickels. How many dimes did she give the postal clerk?

decaine97 said:

1) Rachel paid $1.45 for postage with nickels and dimes. She gave to postal clerk 7 more more than dimes than nickels. How many dimes did she give the postal clerk?

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When solving this type of problem, be sure to distinguish the difference between the NUMBER of coins and the VALUE of the coins. ALWAYS start by naming things.
You have not told us whether you are to use one equation with one variable, or solve two equations simultaneously.
In either case, The value of the nickels is .05 times the number of nickels and the value of the dimes is .10 times the number of dimes.
So if you are to use one equation in one unknown then you start by naming either the number of nickels or the number of dimes...

Let d represent the number of dimes.
Then .10d represents the value of the dimes.
And the number of nickels is d-7.
You can take it from there. Name the value of the nickels and then build your equation using fact that the total value is value of nickels plus the value of the dimes.

If you can build two equations and solve simultaneously, start by naming stuff, possibly like this...

Let number of nickels be n.
Let number of dimes be d.
Value of nickels = .05n.
Value of dimes = .10d.
Now build two equations, one on basis that the number of dimes is 7 greater than the number of nickels, and the other equation based on the fact that their total value is 1.45.

Have at it and be successful.

I just do this:

5N + 10D = 145 (cents)

and from "She gave to postal clerk 7 more more than dimes than nickels" we know the relationship between N and D.

2 variables and 2 equations.