Question 1026655
Let p = original price of the item, and r = rate of increase/decrease.

==> P(1+r) = 3100 and P(1-r) = 1900, as per given information.

Divide the first equation by the second equation (divide corresponding sides.)

==> {{{(1+r)/(1-r) = 31/19}}}
==> {{{19 + 19r = 31 - 31r}}}
==> {{{50r = 12}}} ==> r = 0.24

==> P(1.24) = 3100 ==> {{{P = 3100/1.24 = 2500}}} after substituting into the first equation.

Therefore, P = P2,500, the original price of the item.