Answer:
[tex]\dfrac{50}{72}[/tex]
Step-by-step explanation:
Let $x be the original price of the computer.
As Armen had no enough money to buy a computer, his mother gave him the rest [tex]\frac{3}{8}[/tex] of the total amount that is [tex]\$\frac{3}{8}x.[/tex] Hence, Armen initially had
[tex]\$x-\$\dfrac{3}{8}x=\$\dfrac{5}{8}x[/tex]
Now, in total (with money his mother gave him) Armen had $x.
Armen noticed that due to the sale, he had one tenth of the original amount more than was needed. So, Arment had [tex]\$\dfrac{1}{10}x[/tex] more.
Then the current price is
[tex]\$x-\$\dfrac{1}{10}x=\$\dfrac{9}{10}x[/tex]
To find what part of the current price [tex]\$\dfrac{9}{10}x[/tex] did Armen initially own [tex]\left(\$\dfrac{5}{8}x\right),[/tex] just divide Armen's amount by current price:
[tex]\dfrac{\frac{5}{8}x}{\frac{9}{10}x}=\dfrac{5}{8}\cdot \dfrac{10}{9}=\dfrac{50}{72}[/tex]
