Answer: Let's use algebra to check if Tim is correct.
Let x be the original price of the jeans.
When the jeans are marked down by 20%, the new price becomes:
x - 0.2x = 0.8x
Tim claims that if we increase the new price by 20%, we will get the original price:
0.8x + 0.2(0.8x) = x
Simplifying the left-hand side:
0.8x + 0.16x = x
0.96x = x
This is not true for all values of x, which means that Tim's claim is not correct.
Let's use the given information that the original price is $200 to find out what the new price is after the 20% discount:
New price = Original price - Discount
New price = $200 - 20% of $200
New price = $200 - $40
New price = $160
If we increase the new price of $160 by 20%, we get:
New price + 20% of new price
$160 + 20% of $160
$160 + $32
$192
This is not equal to the original price of $200, so we can conclude that Tim's claim is incorrect.