Question

If a number is increased by 50% then the resultant number is decreased by 40%.
What was the intial number if the final number is 8 less than the original.

Answer 1

If a number is increased by 50%

translated "a number" to x (x for unknown)
increased by 50% means add 50% of x to x:
x + 50% of x

50% of x is written 0.50*x or just 0.5x

so
a number is increased by 50% becomes: x+0.5x
if we factor out the x: (1+0.5)x
add 1+0.5 to get 1.5, and we get 1.5x

a number is increased by 50% becomes 1.5x

Answer 2

then the resultant number is decreased by 40%.

if we have a number (call it y for the time being)
and decrease it by 40% we do this: y - 40% of y
or
y - 0.4*y
or
(1-0.4)y
or
0.6y

that means
to decrease a number by 40% , multiply it by 0.6

then the resultant number is decreased by 40%.
the "resultant number" from the first step is 1.5x
to decrease it by 40% we multiply by 0.6

0.6*1.5x = 0.9x

Answer 3

What was the intial number if the final number is 8 less than the original.

the initial number is x
the final number is 0.9x

the final number is 8 less than the original.
8 less than the original means original - 8 or x - 8

final number is 8 less than the original
0.9x = x - 8

or
0.9x = x -8

can you solve for x ?

Answer 4

Yes. I can solve for x.. thanks.