To find the cost of a hamburger and a hot dog, we can set up a system of equations based on the information provided.
Let \( H \) be the cost of a hamburger and \( D \) be the cost of a hot dog.
From Day 1, the equations are: \[ 200H + 150D = 1450 \] From Day 2, the equations are: \[ 200H + 250D = 1750 \]
Now we can solve this system of equations. First, we can simplify both equations.
Starting from Day 1: \[ 200H + 150D = 1450 \quad \text{(1)} \] From Day 2: \[ 200H + 250D = 1750 \quad \text{(2)} \]
Next, we can eliminate \( 200H \) by subtracting equation (1) from equation (2): \[ (200H + 250D) - (200H + 150D) = 1750 - 1450 \] This simplifies to: \[ 250D - 150D = 300 \] \[ 100D = 300 \] So, we find: \[ D = \frac{300}{100} = 3 \]
Now that we have the cost of a hot dog \( D = 3 \), we can substitute \( D \) back into one of the original equations to find \( H \). We can use equation (1): \[ 200H + 150(3) = 1450 \] This simplifies to: \[ 200H + 450 = 1450 \] Subtracting 450 from both sides: \[ 200H = 1450 - 450 \] \[ 200H = 1000 \] Dividing both sides by 200: \[ H = \frac{1000}{200} = 5 \]
Thus, the cost of a hamburger is $5 and the cost of a hot dog is $3.
So, the final answers are:
- Hamburger: $5
- Hot dog: $3