Lianne charged twice as much to walk a large dog than she did to walk a small dog. this week she had time to was 10 small dogs and 5 large dogs, and she wants to make $100. how much should she charge per small dog? per large dog?

Well she charged twice as much to walk large then small. Let s be small and l be large.
We we know that
l = 2s

we also know that she wants to make 100 so
xl + ys = 100

Where where x is number of large and y is number of small. it says she walked 10 small and 5 large so
5l + 10s = 100

substitute 2s for l because they are same value as shown in first equation I made
5 (2s) + 10s = 100
10s + 10s = 100
20s = 100
s = 5

we can now solve for l
l = 2s
l = 2 * 5
l = 10

So s is 5 and l is 10.