Solving this problem comes down to breaking up what you know into variables and solving them. So what do we know? Well...
1. Mary has a jar containing 55 coins. Some are dimes, and the rest nickels.
To translate the statement into an equation you could say:
numberOfDimes + numberOfNickels = 55 OR
d + n = 55
2. Some are dimes, and the rest nickels. which total $4.50
Translating this statement you need to understand we are looking at the value of the coins. Here you could say:
valueOfDimes + valueOfNickels = $4.50 OR
.1d + .05n = 4.50 multiplying it all by 100 to give nicer numbers say 10d + 5n = 450
3. How many dimes are there?
From here you have your equation, you just need to solve for d. To do that:
Solve for one variable. Just pick n or d and get it alone on one side:
d + n = 55 so n = 55 - d
Plug the value of n into your second equation:
10d + 5n = 450 =>
10d + 5(55 - d) = 450 =>
10d + 275 - 5d = 450 =>
5d + 275 = 450 =>
5d = 175
d = 35
That's all there is too it!
