Let x represent the weight at which the two shipping methods will cost the same amount.
From the information given, the first shipping company charges a fee of $19 to ship a medium box, plus an additional $2 per pound. This means that if we ship an item weighing x pounds using this company, the cost would be
2x + 19
The second shipping company charges $11 for the same size of box, plus an additional $4 per pound. This means that if we ship an item weighing x pounds using this company, the cost would be
4x + 11
For the two costs to be the same, it means that
2x + 19 = 4x + 11
4x - 2x = 19 - 11
2x = 8
x = 8/2
x = 4
We would find the cost by substituting x = 4 into any of the expressions. We have
cost = 2(4) + 19 = 8 + 19 = 27
The two shipping methods both cost $27 at a weight of 4 pounds