# Eighty-one less than 8 times a number is 31. What is the number?

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Let the number be x:

Then:

81 less that 8 times x = 31

==> 8x -81= 31

Add 81 from to sides:

==> 8x = 112

==> Now divide by 8:

==> x= 112/8 = 14

==> x= 14

Then number is 14.

Let the number you need to determine be X.

Now as eighty one less than 8 times the number is 31, we can create an equation as follows:

eight times the number is 8X

eighty one less than eight times the number is 8X-81

as this is equal to 31, we have 8X-81=31

=>8X = 81+31 = 112

=>X= 112/8 = 14

The required number is 14.

We can set up an algebriac equation and solve. Or we can directly solve for by reversing the operations:

Since 81 less than 8 times a number could be lwritten like: 8x-81 . This nimber is coted to be equal to 31. So,

8x- 81 = 31.

To solve this add 81 to both sidees:

8x = 31+81 = 112

Divide by 8 both sides:

8x/8 = 112/8 = 14

x = 14.

Tally:

LHS = 8*14-81 =112-81 = 31 = RHS.

Let the required number = x

Then eight time that number = 8x

And eighty-one less than that = 8x - 81

This is given to be = 31

Therefore:

8x - 81 = 31

Shifting - 81 from left hand side of equation to the right hand side:

==> 8x = 31 + 81

==> 8x = 112

Dividing bot sides by 8:

x = 112/8 = 14

Answer:

The number is 14.