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? Explain.
Let's rewrite the second equation. [tex] \frac{2}{3} p=q[/tex] Multiplying both sides by [tex] \frac{3}{2} [/tex] gives us [tex] \frac{3}{2} \cdot \frac{2}{3}p= \frac{3}{2}q\\
p= \frac{3}{2}q [/tex]
So the second equation is equivalent to the first equation. That means both equations represent the same proportional relationship. Cayley was correct.