Question

c. when a group of ratios are equivalent, it means there is a proportional relationship between the quantities. is there a proportional relationship between the pounds of hay eaten daily and the number of horses? explain.

Explanation:

Step1: Define proportional relationship

A proportional relationship between two quantities \(x\) (number of horses) and \(y\) (pounds of hay) means \(y = kx\), where \(k\) is the constant of proportionality.

Step2: Assume values

Let's assume each horse eats \(h\) pounds of hay per day. If there are \(x\) horses, the total pounds of hay eaten per day \(y=h\times x\). Here, \(h\) is a constant (the amount of hay one horse eats per day).

Answer:

Yes, there is a proportional relationship. If each horse eats a constant amount of hay per day, say \(h\) pounds, and the number of horses is \(x\), the pounds of hay eaten \(y = hx\), which is in the form of a proportional relationship \(y=kx\) (where \(k = h\)).