When a number is decreased by 30% of​ itself, the result is 63. What is the​ number?

Question

When a number is decreased by 30% of​ itself, the result is 63. What is the​ number?

Answer 1

When you decrease anything by 30%, you are left with 70%, right?

0.7x = 63

x = 90

Answer 2

X + 30% * X = 63 <--- increased by 30% of itself is 63, as GIVEN

1*X + 30% * X = 63 <-- understood to be coefficient of 1

100% * X + 30% * X = 63 <-- 1 = 100%, or ALL OF IT

130% * X = 63 <-- combines like terms

130/100 * X = 63 <-- changes 130% to fraction

X = 63*100/130 <---- multiplies both sides by the reciprocal 100/130; fraction on left cancelled out

= 63*10/13 <-- reduces by factor of 10

= 630/13

= 48 + 6/13 <-- changes to mixed fraction

check

130% is 30% INCREASE, which is 130/100

130*100 * (630/13) = (130*630)/(100*13)

= (13*63)/13 <-- 100 cancels factors of 10 from 130 and 630

= 63 <-- 13 cancels out