If x represents the cost of burger meals, then y represents the cost of a hot dog meal.
The system of linear equations would look like:
3x + 4y = 48
6x + 2y = 60
To solve for x and y, we can multiply the first equation by 2 and the second equation by 2 to eliminate y:
6x + 8y = 96
12x + 4y = 120
Subtracting the second equation from the first equation gives:
-6x + 4y = -24
Dividing both sides by -2, we get:
3x - 2y = 12
Adding this equation to the second equation gives:
6x + 2y = 60
3x - 2y = 12
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9x = 72
x = 8
Therefore, a burger meal costs $8. To find the cost of a hot dog meal, we can substitute x = 8 into the first equation:
3(8) + 4y = 48
24 + 4y = 48
4y = 24
y = 6
Therefore, a hot dog meal costs $6.
The total $ spent on both meals would be:
3(8) + 4(6) = $24 + $24 = $48
Therefore, the answers are:
- The cost of a burger meal: $8
- The cost of a hot dog meal: $6