Question

PLEASE HELP ME‼️

At a concession stand three hot dogs and four hamburgers cost $11.50

four hot dogs and three hamburgers cost $11.25

Find the cost of one hot dog and the cost of one hamburger

Answer 1

One hot dog costs $1.50 and one hamburger costs $1.75

Explanation:

Let x be the cost of one hot dog and y be the cost of one hamburger.

From the first statement, we can set up the following equation:

3x + 4y = 11.5

Similarly, from the second statement, we can set up another equation:

4x + 3y = 11.25

Now we have two equations with two variables. We can solve for x and y using algebraic methods.

One way to do this is to use elimination. We can multiply the first equation by 4 and the second equation by 3, so that we can eliminate one of the variables:

12x + 16y = 46

12x + 9y = 33.75

Subtracting the second equation from the first, we get:

7y = 12.25

Dividing both sides by 7, we get:

y = 1.75

Now we can substitute y = 1.75 into either of the original equations to solve for x. Let's use the first equation:

3x + 4(1.75) = 11.5

3x + 7 = 11.5

3x = 4.5

x = 1.5

Therefore, one hot dog costs $1.50 and one hamburger costs $1.75.