Final answer:
To find the cost of each hot dog when a student buys two hot dogs and three drinks for $5.25, set up equations based on the given information. After solving the equations, it is determined that each hot dog costs $1.50.
Step-by-step explanation:
To solve the problem where a student buys two hot dogs and three drinks for $5.25, with drinks costing half as much as the hot dogs, we need to set up two equations. Let's denote the cost of a hot dog as x and the cost of a drink as y.
Since we know that the drink costs half as much as the hot dog, the following equation can be established: y = 0.5x.
We also know that the total cost for two hot dogs and three drinks is $5.25, giving us the equation: 2x + 3y = 5.25.
Substituting the expression for y into the second equation gives: 2x + 3(0.5x) = 5.25, which simplifies to 3.5x = 5.25. Dividing both sides of the equation by 3.5 gives x = 1.5. Therefore, the cost of each hot dog is $1.50, which corresponds to option D.