Notebooks

Take the initial amount to be $100, therefore Rodrigo's, total expenditure was $240 and Gustavo's total expenditure was $300.

- To find out how much less % of money Rodrigo spent than Gustavo

JUST DO THIS :-

Let $£ =$ Price of notebook , $a =$ Answer (%)

The first notebook bought by Rodrigo ( $r$ ) cost $100$ % of the price, the second one cost $(100 - 20)$ % and the last cost $(100 - 40)$ % so adding these together gives

$100 + (100 - 20) + (100 - 40) = 240$

(That's $240$ % of $£$ ). This can also be written as $2.4£$

Let $r = 2.4£$

All three notebooks bought by Gustavo ( $g$ ) are the full price so ( $3 \cdot 100$ % )

$100 \cdot 3 = 300$

(As with before this is $300$ % of $£$ ). This can also be written as $3£$

Let $g = 3£$

Next we find what $a$ equals by using the following formula

$a = (1 - \frac {r}{g}) \cdot 100$

( $\frac {r}{g} \cdot 100$ is what percentage $r$ is of $g$ ) Since we know what $r$ and $g$ equal we can sub the values in

$a = (1 - \frac {2.4£}{3£}) \cdot 100$

The $£$ s cancel out leaving

$a = (1 - \frac {2.4}{3}) \cdot 100$

Simplifying the brackets gives us

$a = \frac {0.6}{3} \cdot 100$

If we then make the fractions denominator equal to $1$ we get

$a = \frac {0.2}{1} \cdot 100$

This becomes

$a = 0.2 \cdot 100$

Which means that $a = 20$

So the answer is $20$ % less