Question

The Highland Booster Club sells refreshments at the concession stand for local football games. Combination 1 includes 4 hot dogs and 2 sodas for $10. Combination 2 includes 6 hot dogs and 3 sodas for $15. Let h represent the cost of a hot dog, and let s represent the cost of a soda. Write the pair of linear equations that model this situation.

Answer 1

To model the situation with linear equations, we need to set up two equations based on the combinations being sold by the Highland Booster Club.

For Combination 1:

• We have 4 hot dogs and 2 sodas, which sell for $10.
• This can be expressed as: \[ 4h + 2s = 10 \]

For Combination 2:

• We have 6 hot dogs and 3 sodas, which sell for $15.
• This can be expressed as: \[ 6h + 3s = 15 \]

Now we have the following pair of linear equations:

1. \( 4h + 2s = 10 \)
2. \( 6h + 3s = 15 \)

These equations can be used to solve for the cost of a hot dog (h) and a soda (s).