#1 - Write clear and thorough definitions. In the equation above, you have 'x'. What does it mean? You must tell your audience what you mean.
#2 - In the equation above, the denomination of the coin is not mentioned in the problem statement. Why would you have 0.25, 0.10, or 0.05 in there? Those are the values of the coins. We're just counting on this one.
#3 - Please get comfortable with multiple variables. If I say D = # of dogs in Kalispel Montana, then that is what it means. If I ask, How may dogs are there in Kalispel?, you can respond "D". My "D" represents that number. It is not some other entity. It is my representative for the number of dogs. More on this "representative" thing, later.
For this problem, I woudl do this:
Q = # of Quarters
D = # of Dimes
N = # of Nickles
#4 - You must learn to translate. One things at a time. Look at each phrase from the problem statement and see how I have translated it in light of my definitions.
"He has a total of 52 coins."
Q + D + N = 52
"three more quarters than dimes"
D + 3 = Q
"five fewer nickels than dimes"
D - 5 = N
Look at each one until you see how it is translated and how the equation relates DIRECTLY to the phrase from whence it came.
#5 - Let the algebra help you. We created symbols and systems to make your life easier. As of this moment, this can be a pure mathematics problem. It does NOT have to be about coins in Sal's pocket. We have three equations and we can deal with them. Do NOT let them scare you. A common method of solution is called "substitution". We have representatives for things. Let's use the representatives.
Here's the three equations:
1) Q + D + N = 52
2) D + 3 = Q
3) D - 5 = N
Equation 1) looks big. Let's pass on it for now.
Wait, Equation 2) can help us. Equation 2) gives us another way to write "Q". Let's use Equation 2) and rewrite Equation 1.
4) (D + 3) + D + N = 52
Look at his very hard until you see the substitution principle working. Since Q = D + 3, I can write either. I choose to write that which is most advantageous to the evential solution.
Aha! We can do the same thing with Equations 3) and 4). Equation 3) gives us another way to write "N".
5) (D + 3) + D + (D - 5) = 52
Again, look very hard until you see how this works.
From here, we tend to call it "simplification". Collect like terms and see how it goes.
(D + 3) + D + (D - 5) = 52
Parentheses are unnecessary in this case.
D + 3 + D + D - 5 = 52
Group the "D"s and the constants on the left-hand side
D + D + D + 3 - 5 = 52
Combine the like terms
3D - 2 = 52
3D = 54
Divide by 3
D = 18
#6 - Go read the problem statement again, just to make sure we are answering the right question.
"How many dimes does Sal have? "
Perfect! That's what we have answered. Sal has 18 dimes.
Just for fun and checking, remember Equations 2) and 3)?
2) D + 3 = Q
3) D - 5 = N
Then Q = 18 + 3 = 21
And N = 18 - 5 = 13
Finally 21 + 18 + 13 = 39 + 13 = 52 - Check!!
Here's the deal. We can't write you a book every day. We can try, but you REALLY need some close personal attention. You can learn it.