Aiden wrote a riddle: Five less than 1/5 times a number is the same as the sum of the number and 1/3. How do you find the number?

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Answer 1 · 2016-12-11T01:07:32

The number is #color(green)(-22.5)#

Let the number be #n#

#{: ("Five less than 1/5 times a number: ",1/5n-5), ("is the same as: ",=), ("the sum of the number and 1/3",n+13) :}#

#1/5n-5=n+13#

Multiply both sides by #5#
#n-25=5n+65#

Subtract #n# from both sides
#-25=4n+65#

Subtract #65# from both sides
#-90=4n#

Divide both sides by #4#
#-22.5=n#

Exchange sides (not necessary, but most people like it better this way)
#n=-22.5#