how to work out an original number if you're given a percentage increase?

A "percentage" is just a fancy way of writing a fraction over 100.

7% is the same as 7/100

Next trick: 1 can be written as any fraction where the top is equal to the bottom (except 0)

1 = 2/2 = 3/3 = ... = 100/100 ... and so on, until you get sick of it.

If the original number was your "unit" (your "one"), then the number, AFTER the increase, is 1 + the increase

An increase of 7 %

means the new number represents 1 + 7/100 = 100/100 + 7/100 = 107/100

of the original number

We will call the original number "x" (simply because it looks good when working out this type of problems - if you prefer a different letter, go ahead).

107 % of x = 1.6

1.07 x = 1.6

divide both sides by 1.07

x = 1.6 / 1.07 = 1.4953271... kg.

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Let's try it with a rounded figure, close to our calculated answer:

The object originally weighed 1.5 kg.

7% of that is (7/100) * 1.5 kg = 0.105 kg

The weight after the increase of 7% is

1.5 + 0.105 = 1.605 kg.

This could be close enough (depending what we are doing), otherwise, it confirms that the real answer is ever-so-slightly below 1.5 kg.

If we start with the calculated weight

x = 1.495327 kg

then 7% of that is 0.104673 kg

107% = 100% + 7% =

1.495327 + 0.104673 = 1.600000 kg

OK you have somethings that weighs w. And it increases in weight so that e = (W - w)/w = .07, which is 7% as a decimal.

So you see this? W = 1.6 kg > w, it's bigger than w. And the bigness (the increase) is 7% of the original weight, which is why there is a w in the denominator.

So all you need do is solve for w, the original weight w from .07w = W - w; so that (1 + .07)w = W and w = W/1.07 = 1.6/1.07 = 1.5 kg ANS.

after a 7% increase you have 107% if the original amount

so

1.07 * X = 1.6 kg

X = 1.4953 kg or 1.5 kg to 2 sig figs

If someone gives you a good answer,

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Find out what 1% is and times it by 100

So 1.6kg / 107% =0.0149...

0.0149... * 100 = 1.50 (to 2 decimal places)

New weight / old weight = 1.07

Plug in new weight and solve for old weight

107/100*m=1.6kg => m=1.6*(100/107) kg