Answer:
based on the information provided, Madelyn has a total of 26 dogs in her animal rescue. Of these, there are 13 smaller dogs who consume a total of 19.5 cups of food per day (1.5 cups per dog), and there are 13 larger dogs who consume a total of 39 cups of food per day (3 cups per dog).
Explanation:
We know that the total number of cups of food consumed by the dogs is 39. We can use this information to create an equation:
1.5s + 3l = 39
We also know that Madelyn has a total number of dogs, which we can represent as:
s + l = total number of dogs
However, we cannot solve for s and l with only one equation. We need another equation to help us solve for both variables.
From the information provided, we know that each smaller dog gets 1.5 cups of food per day and each larger dog gets 3 cups of food per day. Therefore, the total amount of food consumed in one day can also be represented as:
1.5s + 3l = total cups of food consumed in one day
Since we know that the total cups of food consumed in one day is equal to 39, we can substitute this value into the equation:
1.5s + 3l = 39
1.5s + 3l = 39
2s + 4l = 52
Now we have two equations with two variables:
s + l = total number of dogs
2s + 4l = 52
We can use substitution or elimination to solve for s and l. Using substitution:
s + l = total number of dogs
s = total number of dogs - l
2(total number of dogs - l) + 4l = 52
2total number of dogs - 2l + 4l = 52
2total number of dogs + 2l = 52
total number of dogs + l = 26
Now we have two equations:
s + l = total number of dogs
total number of dogs + l = 26
We can use substitution again:
s + l = total number of dogs
s = total number of dogs - l
(total number of dogs - l) + l = 26
total number of dogs = 26
Therefore, Madelyn has a total of 26 dogs. We can now solve for the number of smaller and larger dogs using one of the previous equations:
s + l = total number of dogs
s + (26 - s) = 26
s = 13
Therefore, Madelyn has 13 smaller dogs and 13 larger dogs.