Question

The population of Norson, the largest city in Transitania, is 50 percent of the rest of the population of Transitania. The population of Norson is what percent of the entire population of Transitania?

Answer 1

if x is the entire population of transitania...

let y = population of norson

it says that the population of norson is 50% of the "rest" of the population

since x is the entire population and y is the population of norson... x - y is the rest of the population

so population of norson is 50% of x - y

so y = 50% of x - y

\[y = \frac{50}{100} (x-y)\]
distribute...
\[y = \frac{50}{100}x - \frac{50}{100} y\]
simplify...
\[y = \frac x2 - \frac y2\]
add y/2 to both sides
\[y + \frac y2 = \frac x2\]
combine like terms
\[\frac{3y}{2} = \frac x2\]
multiply both sides by 2
\[3y = x\]since x is the ENTIRE population and y is the population of NORSON that means the entire popilation 300% of the population of norson

got it @ksaimouli ?