Andres has 10 more goldfish than todd. together, they have 50 goldfish. how many goldfish does each boy have?

Let's go ahead and construct an equation to show this. Together, they have 50 goldfish. This can be represented as =50. 

Since we don't know how many Todd has, we're going to make a variable. We'll name it T, for Todd.

What about Andres? How many does he have? 10 more than Todd. Well, if Todd's amount is T, and Andres has 10 more, we can express that as T+10.

Now, just put the two pieces together! T+10=50. 

The next step is inverse operations. You want to find out how many T is, so you need to get rid of the 10. To take 10 away from something is doing what? Subtraction! Be warned, though; whatever you do to one side of the problem, you have to do to the other. 10-10 is 0, and 50-10 is 40. Since we took the 10 away and 50 is now 40, what you're left with is T=40.

Wait a second.. wasn't "T" Todd's amount? Yep! That means that Todd has 40 goldfish. And we already know that Andres has 10, so there's your answer!

Let Todd's fish = T

that would make

Andres fish = T + 10.

Together they have 50 fish so...
T + (T +10) = 50
2T + 10 = 50
2T = 40
T = 20

so Todd has 20 fish.

Remember Andres has
T + 10 fish, so...

T + 10 =
20 + 10 = 30

Andres has 30 fish

Check the problem by plugging the numbers into the original equation...

T + T + 10 = 50
20 + 20 + 10 = 50
50 = 50

It checks!