One half of a number increased by 16 is four less than two thirds of the number. What are the numbers?
February 20th, 2023
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##