Optimization in two variables and Lagrange multipliers practice question 3

What is being maximised, and what is the constraint? Turn the two prices and the $100 budget into an equation in $x$ and $y$.

The budget is $2x + 5y = 100$. The Lagrange conditions $U_x = \lambda g_x$ and $U_y = \lambda g_y$, with $g(x, y) = 2x + 5y$, read $y = 2\lambda$ and $x = 5\lambda$.

Substitute $x = 5\lambda$ and $y = 2\lambda$ into the budget to find $\lambda$, then $x$ and $y$, then $U$.