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

1 Answer
Alan P. ยท EZ as pi
Oct 24, 2016

The number is color(green)(72)

Explanation:

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

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