To find the number of horses that the trainer can train with the 42 mints, we can set up an equation based on the number of mints and the number of treats needed per session for each horse.
Let \( h \) be the number of horses she can train. Since each training session requires 5 treats per horse, the total number of mints used for \( h \) horses will be \( 5h \). We know she has 42 mints available.
The equation can be set up as follows:
\[ 5h \leq 42 \]
Now, to find the maximum number of horses \( h \) she can train, we can solve for \( h \):
\[ h \leq \frac{42}{5} \]
Calculating that gives:
\[ h \leq 8.4 \]
Since the number of horses must be a whole number, she can train a maximum of 8 horses.
To verify this, if she trains 8 horses, the total number of mints needed would be:
\[ 5 \times 8 = 40 \text{ mints} \]
Since 40 mints are used, she will have 2 mints remaining, which is acceptable. If she were to train 9 horses, the total treats needed would be:
\[ 5 \times 9 = 45 \text{ mints} \]
This exceeds the 42 mints available, hence she cannot train 9 horses.
Therefore, the equation that shows the number of horses she can train is:
\[ 5h \leq 42 \]
And the viable solution for the number of horses \( h \) is 0 to 8.