Final answer:
The student's question involves solving a system of linear equations to find the cost of hamburgers. By simplifying and substituting equations, it is determined that each hamburger costs $2.
Step-by-step explanation:
The student's question is about determining the cost of hamburgers given a system of linear equations. According to the first equation derived from the given information, the cost of ten hot dogs (10d) is the same as the cost of five hamburgers (5b), which gives us the equation 10d = 5b. This can be simplified to 2d = b. The second piece of information tells us that the cost of four hamburgers and six hot dogs (4b + 6d) equals $14, represented by the equation 4b + 6d = $14.
To find the cost of hamburgers, we first substitute the value of b from the first equation into the second equation to get 4(2d) + 6d = $14, resulting in 14d = $14. Dividing both sides of the equation by 14 gives us d = $1, which means one hot dog costs $1. Plugging this back into the first equation, we get 2(1) = b, so b = $2. Therefore, each hamburger costs $2.