Cayley says the the equations q=1.5q and 2/3p=q both represent the same proportional relationship. Mariah says that cant be true because the constant proportionality are different. With which student do you agree?Explain.

Cayley says that the equations p=1.5q and 2/3p=q both represent the same proportional relationship. Mariah says that can't be true because the constants of proportionality are different. With which student do you agree?

we know that

A relationship between two variables, p, and q, represent a proportional variation if it can be expressed in the form [tex]k=\frac{q}{p}[/tex] or [tex]q=kp[/tex]

In this problem we have

[tex]p=1.5q[/tex] ----> equation A

[tex]q=\frac{2}{3}p[/tex] ---> equation B

Rewrite the equation A

solve for q ----> That means, isolate the variable q

Divide by 1.5 both sides (remember that 1.5=3/2)

[tex]p/(3/2)=q[/tex]

so

[tex]q=\frac{2}{3}p[/tex] ----> equation A

Equation A and equation B represent the same line

therefore

The constant of proportionality is the same in both equations

Both represent the same proportional relationship

Cayley was correct