Real-World Systems of Equations Practice
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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.
Equation for Combination 1: = 10
Equation for Combination 2: = 15
Equation for Combination 1: 4h + 2s = 10
Equation for Combination 2: 6h + 3s = 15
Equation for Combination 1: 4h + 2s = 10
Equation for Combination 2: 6h + 3s = 15
To write the pair of linear equations that model this situation, we need to define the variables and set up the equations based on the given information.
Let's denote the cost of a hot dog as "h" and the cost of a soda as "s".
From the problem, we are given the following information:
Combination 1 includes 4 hot dogs and 2 sodas for a total cost of $10.
Combination 2 includes 6 hot dogs and 3 sodas for a total cost of $15.
From this information, we can set up two equations:
Equation 1: 4h + 2s = 10 (for Combination 1)
Equation 2: 6h + 3s = 15 (for Combination 2)
In Equation 1, we multiply the cost of a hot dog by 4 (since there are 4 hot dogs) and the cost of a soda by 2 (since there are 2 sodas). The sum of these products equals $10.
In Equation 2, we multiply the cost of a hot dog by 6 (since there are 6 hot dogs) and the cost of a soda by 3 (since there are 3 sodas). The sum of these products equals $15.
So, the pair of linear equations that model this situation is:
Equation for Combination 1: 4h + 2s = 10
Equation for Combination 2: 6h + 3s = 15