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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?

Answer 1

Savannah Anderson

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#

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Answer 2

Abigail Allen

Let the number be represented by x.

Translate the given riddle into an equation:

1/5 * x - 5 = x + 1/3

Now, solve for x:

1/5 * x - x = 1/3 + 5

(1/5 - 1) * x = 1/3 + 5

(-4/5) * x = 16/3

Multiply both sides by -5/4 to isolate x:

x = (16/3) * (-5/4)

x = -20/3

Therefore, the number is -20/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.