Math question about [hard] percents!

the owner of a store buys goods at 35% off the list price. she marks them so that after giving a discount of 20%, she will still make a profit of 10% of the marked price. She makes $13 on the sale of each item. what is the list price?

please give a thorough explanation for this problem.
thank you in advance! :)

13 is 10% of the marked price so 13/m = 10/100
10m = 1300
m = 130.

This is 80% of what she buys them for, since its been reduced by 20%. So
80/100 = 130/b
80b = 13000
b = 162.50 which is 65% of the list price since it was 35% off. So
162.50 / L = 65/100
65L = 16250
L = $250

Let the list price = x

Let the marked price = y

0.80(y) - 0.65(x) = 0.1(y)

We know that since she makes $13 on the sale of each item, 0.10(y) = 13, then:

13(8) - 0.65(x) = 13

x = $140

Let x=list price

She buys it for 0.65 x

I will put it all in one equation

Profit=0.1[0.65x-(0.2)(0.65x)]

13=0.1[0.65x -0.13x]

13=0.1(0.52x)

13=0.052x

x=13/0.052

x=$250 the list price

Is it $130 , cause 13 dollars is the 10 percent profit , so 100 percent is 130 dollars