A GROUP OF STUDENTS GO OUT TO LUNCH. IF TWO HAVE HAMBURGERS AND FIVE HAVE HOT DOGS, THE BILL WILL BE $8.00. IF FIVE HAVE HAMBURGERS AND TWO HOT DOGS, THE BILL WILL BE $9.50. WOULDNT THE ANSWER BE $1.50

But -- what is the question?

THE QUESTION IS ASKING ME TO FIND THE COST OF A HAMBURGER?

is your keyboard broken???

lol it is $1.50

To solve this problem, we can assign variables to represent the cost of a hamburger and the cost of a hot dog. Let's say the cost of a hamburger is "h" and the cost of a hot dog is "d".

According to the given information, if two students have hamburgers and five have hot dogs, the bill is $8.00. So we can write an equation based on this:
2h + 5d = 8.00 ----(Equation 1)

Similarly, if five students have hamburgers and two have hot dogs, the bill is $9.50. So we can write the second equation:
5h + 2d = 9.50 ----(Equation 2)

To find the values of "h" and "d", we need to solve these two equations simultaneously.

One way to do this is by using the method of substitution. First, solve Equation 1 for "h":
2h = 8.00 - 5d
h = (8.00 - 5d) / 2 ----(Equation 3)

Now, substitute Equation 3 into Equation 2:
5[(8.00 - 5d) / 2] + 2d = 9.50

Simplify and solve for "d":
(40.00 - 25d + 2d) / 2 = 9.50
40.00 - 25d + 2d = 19.00
-23d = -21.00
d = (-21.00) / (-23)
d ≈ 0.9130

Now, substitute the value of "d" back into Equation 3 to find the value of "h":
h = (8.00 - 5 * 0.9130) / 2
h = (8.00 - 4.565) / 2
h ≈ 1.7175

So, the cost of a hamburger (h) is approximately $1.72 and the cost of a hot dog (d) is approximately $0.91.

Now, let's calculate the total bill when the group orders 5 hamburgers and 2 hot dogs:
5h + 2d = 5 * 1.72 + 2 * 0.91
= 8.60 + 1.82
= $10.42

Therefore, the answer is not $1.50, but rather $10.42.