Robert has a collection of 26 fishing lures and Lucy has a collection of 34 fishing lures. Robert is adding 4 new lures per month to his collection, while Lucy is adding 2 new lures per month to her collection. After how many months will Robert and Lucy have the same number of fishing lures? Write and solve a system of equations.
Let $x$ be the number of months. It is given that Robert adds 4 lures per month and starts off with 26 lures. Hence, the total number of lures Robert has after $x$ months is $26+4x$. It is also given that Lucy adds 2 lures per month and starts off with 34 lures. Hence, the total number of lures Lucy has after $x$ months is $34+2x$. Hence, we have the equation $26+4x=34+2x$. Subtracting $2x$ and $26$ from both sides gives $4x-2x=34-26$, or $2x=8$. Hence, $x=\boxed{4}$ months.
