At a local shelter large dogs can be adopted for $10 each. small dogs can be adopted for $5 each. there are 17 large dogs available for adoption. if all the dogs are adopted the shelter will make $215.describe a strategy to find the number of small dogs at the shelter

You first want to make the word problem into equations!

Let x represent large dogs
Let y represent small dogs.

10x+5y=215

And now since you are given the value of x / the number of dogs you can solve by subbing this value into the equation.

10(17)+5y=215
170+5y=215
5y=215-170
5y5=45/5
y=9

So as you can see there are 9 small dogs at the shelter!

Explanation #2 

In the word problem you can see that it tells you that there is 17 large dogs. It also tells you that in total all the dogs (so large and small) will be $215. It also says the prices of the dogs!

So what you know is : 17 large dogs, $215 total, $5 for a small dog, $10 for a large dog!

In order to figure out how many small dogs are at the shelter you will need to make this information into an equation!

Since it is 10/ large dog this is 10x
Since it is 5/small dog this is 5y

So now you know that 10x+5y=215

Since you are given the # of large dogs, you can put in that number for x

10(17)+5y=215  

170+5y=215   Step 1) Multiply 10 x 17
5y=215-170    Step 2) Move everything without a letter to one side
5y/5=45/5       Step 3) Divide by 5 (Both sides!) to get the y all alone
y=9                 Step 4) All done!

There would be 8 small dog keep adding 5 to 170 and the answer would be 8 5s away :)