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A man spends one fifth of the money in his wallet . He then spends one fifth of what remains in the wallet. He spends $36.00 in all. How much money did he have to begin with?

x = Money to begin

\(\begin{array}{c|l|r} \hline & \text{wallet} &\text{giving dollar} \\ \hline & x & 0 \\ &(x)-\frac15\cdot x & \frac15\cdot x \\ &(x-\frac15\cdot x) -\frac15(x-\frac15\cdot x) & \frac15(x-\frac15\cdot x)\\ \hline \text{sum} && $36\\ \hline \end{array}\)

\(\begin{array}{rcl} \frac15\cdot x + \frac15(x-\frac15\cdot x) &=& $36 \quad & | \qquad \cdot 5 \\ x + x-\frac15\cdot x &=& $180 \\ 2x-\frac15\cdot x &=& $180 \quad & | \qquad \cdot 5 \\ 10x-x &=& $900 \\ 9x &=& $900 \quad & | \qquad :9 \\ \mathbf{ x } & \mathbf{=} & \mathbf{$100} \\ \end{array}\)

To begin he has $100.

\(\begin{array}{c|l|r} \hline & \text{wallet} &\text{giving dollar} \\ \hline & \mathbf{$100} & 0 \\ & $100-$20=$80 & \frac{$100}{5}=$20 \\ & $80-$16=$64 & \frac{$80}{5} =$16\\ \hline \text{sum} && $36\\ \hline \end{array}\)

Let x  be the amount he started with

So....he first spends  1/5 of this  = (1/5)x

So....what's left  =   (4/5)x

And he spends (1/5)  of this  = (1/5)(4/5)x =  (4/25)x

So  he spends   (1/5)x + (4/25)x   and this = $36.......so we have

(1/5)x + (4/25)x  = 36

(5/25)x + (4/25)x   = 36

(9/25)x   = 36      multiply both sides by  25/9

x =36 (25/9)

x = (36/9) * 25

x = 4 * 25   =   $100       and this is what he started with

Proof......he spends  1/5 of  $100  = $ 20

Then....he spends 1/5 of  what's left = (1/5)($80)  = $16

And $20 + $16   = $36

Let the original amount=x

.8x remains after 1st 1/5 spent.

.8 x .8x=.36x remains after the 2nd 1/5 spent

.36x=36

x=$100 orignal amount he started with