An algebra problem by Ahmed Mahmoud

Let $x$ be the initial amount of money of Mr. Money in the bank.

On the first year, it decreased by $25\%$ .

$x-0.25x=0.75x$ $\implies$ amount of money after it was decreased by $25\%$

It increased by $20\%$ on the second year.

$0.75x+0.2(0.75x)=0.9x$ $\implies$ amount of money after it was increased by $20\%$

It decreased by $10\%$ on the third year.

$0.9x-0.1(0.9x)=0.81x$ $\implies$ amount of money after it was decreased by $10\%$

It increased by $20\%$ on the fourth year.

$0.81x+0.2(0.81)=0.972x$ $\implies$ amount of money after it was increased by $20\%$

So the money decreased by $1-0.972=0.028$ or $\boxed{2.8\%}$ .

Let P0 denote the amount of money Mr. Money has in his bank account. Let Pi denote the amount of money remaining in Mr. Money’s account after i years. Then we know that

P1 = 3/4P0

P2 = 12/10P1 = 9/10P0

P3 = 9/10P2 = 81/100P0

P4 = 12/10P3 = 243/250P0:

Hence Mr. Money’s account has decreased by 7/250P0. That is, it decreases by 2:8%