A horse trainer has some treats. She needs 5 treats per training session. The bag holds 42 treats. Which equation shows the number of horses that she can train and is the solution viable?

Question

For me: I think the equation is 5h=42 =8.4 horses. It would be viable, because if you substitute the 8.4 for h, it gives you 42, and I know I cannot have 8.4 horses, but I can have 8 horses. Is this correct?

Answer 1

Let's break it down step by step.

1. Understand the problem: The horse trainer needs 5 treats per training session, and she has a bag that holds 42 treats. We want to find out how many horses (or training sessions) she can train with those 42 treats.

2. Setting up the equation: Let \( h \) be the number of horses she can train. Since she needs 5 treats per horse, the equation for the total number of treats needed is: \[ 5h = 42 \]

3. Solving for \( h \): To find the number of horses, we divide both sides of the equation by 5: \[ h = \frac{42}{5} = 8.4 \]

4. Interpreting the result: The value of \( h = 8.4 \) indicates that she cannot train 8.4 horses, as the number of horses must be a whole number. Therefore, she can only train a maximum of 8 horses completely.

5. Conclusion: The equation \( 5h = 42 \) is correct, and while the solution \( h = 8.4 \) indicates the exact division, it is not viable in practice since you cannot have a fraction of a horse. Thus, the maximum number of horses she can train would be 8, as this would use \( 5 \times 8 = 40 \) treats, leaving her with 2 treats remaining.

To summarize, the equation is correct, but while 8.4 horses is the mathematical solution, it is practically rounded down to 8 horses.

Answer 2

So, with this you mean that the answer would have to be "not viable" just because it is not a whole number?

Answer 3

Yes, that's correct. In the context of this problem, the solution of 8.4 horses is not viable because you cannot train a fraction of a horse.

Viability in this case refers to the practical application of the solution:

• Mathematically, the equation \( 5h = 42 \) gives us the exact division \( h = 8.4 \).
• Practically, since you can't train a partial horse, you must consider only whole numbers. Therefore, the highest viable number of horses the trainer can train, based on her available treats, is 8.

So, while the mathematical solution indicates 8.4, the practical answer is that you can only train 8 horses. Thus, we conclude that in this scenario, "not viable" would be the appropriate way to describe the solution of 8.4 horses. The maximum viable answer is 8 horses.

Answer 4

Thank you.

Answer 5

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy training!