One half of a number increased by 16 is four less than two thirds of the number. What are the numbers?

The number is ##color(green)(72)##

Let the number be ##n##

the number increased by ##16## ##color(white)("XXX")n+16##

one half of the number increased by ##16## ##color(white)("XXX")1/2(n+16)##

two thirds of the number ##color(white)("XXX")2/3n##

one half of the number increased by ##16## is ##4## less than two thirds of the number ##color(white)("XXX")1/2(n+16)=2/3n-4##

Multiply both sides by ##6## to get rid of the fractions ##color(white)("XXX")3(n+16)=4n-24##

Simplify ##color(white)("XXX")3n+48=4n-24##

Subtract ##3n## from both sides ##color(white)("XXX")48=n-24##

Add ##24## to both sides ##color(white)("XXX")72=n## or ##color(white)("XXX")n=72##