Problem Solving

If the function Q is defined by the formula Q=5w/4xz^2, by what factor will Q be multiplied if w is quadrupled, x is doubled, and z is tripled?


The answer is given in Manhattan Review but failed to understand. Please help!

Q=5w/4xz^2

Let's first see how each action affects Q individually and then we'll combine them.

Quadrupling means w is replaced by 4w. Replacing w with 4w in the above equation gives:
Q=5(4w)/4xz^2
=4*5w/4xz^2
=4Q

So quadrupling w quadruples Q.

Doubling x means x is replaced by 2x:
Q=5w/4(2x)z^2
=(1/2)(5w/4xz^2)
=(1/2)Q

So doubling x halves Q.

Tripling z means z is replaced by 3z:

Q=5w/4x(3z)^2
=5w/4x*9z^2
=(1/9)(5w/4xz^2)
=(1/9)Q

So tripling Z multiplies Q by 1/9

Taking all of these things together:

Q is multiplied by 4*(1/2)*(1/9)=2/9

Your other option is to just make up simple numbers for w,x, and z, plug them in, see what Q is. Then do the quadrupling, doubling and tripling, plug them in again and see what the new result is, and compare.

To see the plugging in approach, check my explanation here:

https://www.beatthegmat.com/function-q-t89639.html

Thanks a lot. Now it is clear to me.