GIVEN: \(\frac{2x}{3}\) always equals \(16yz\)

We can write: \(\frac{2x}{3}=16yz\)

Multiply both sides of the equation by 3 to get: \(2x=48yz\)

Divide both sides of the equation by 2 to get: \(x=24yz\)

If y is tripled and z is halved, then x is
A fast way to answer this question is by testing some values

If \(y=1\) and \(z=2\), then \(x=24yz = 24(1)(2)=48\)
So, when \(y=1\) and \(z=2\), \(x=48\)


If y is tripled and z is halved, then \(y=3\) and \(z=1\)
Plugging these values into our equation we get: \(x=24yz = 24(3)(1)=72\)

To answer the question we need to determine the percent increase from 48 to 72.

Percent increase \(= \frac{(100)(72-48)}{48}\)

\(= \frac{(100)(24)}{48}\)

\(= \frac{(100)(1)}{2}\)

\(= 50\) percent

Answer: E

Cheers,
Brent
_________________

There is a simpler way to solve such types of exercises. First of all you should indicate x. Rewrite the equation (2x)/3=16yz as x=(3*16*y*z)/2. Then multiply y by 3 and divide z by 2 and you get the following expression: x=(3*16*y*z)/2 * (3/2). Now 3/2 equals 1.5 which in terms of percentage connotes an increase by 50%. So E)

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