at a baseball concession stand 3 hot dogs and 2 cups of soda together cost 13.50. two hot dogs and 1 cup.of soda together costs 8 select all statements that are true about this situation.
A. Each hot dog costs 2.50
B. Each cup of soda costs 3.50
C. The total cost of 3 hot dogs and 2 cups of soda can be modeled by the equations 3x+2y=13.50
D. The total cost of 2 hot dogs and 1 cups of soda can be modeled by the equation 3y=8
3 x + 2 y = 13.5
2 x + 1 y = 8
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3 x + 2 y = 13.5
4 x + 2 y = 16
-----------------subtract
- x = - 2.5
x = 2.50 for hot dog (A yes)
then
5 + y = 8
y = 3.00 for soda (B no )
C yes, that is what I did
D makes no sense at all
To find the statements that are true about the situation, let's analyze the given information.
We are given that 3 hot dogs and 2 cups of soda together cost 13.50, and that two hot dogs and 1 cup of soda together cost 8.
A. To determine if the statement "Each hot dog costs 2.50" is true, we can set up an equation using the given information. Let's assume the cost of each hot dog is x and the cost of each cup of soda is y.
We are given that 3 hot dogs and 2 cups of soda together cost 13.50, so the equation would be:
3x + 2y = 13.50
Now, we can try to substitute the value of x = 2.50 and see if the equation holds true:
3(2.50) + 2y = 13.50
7.50 + 2y = 13.50
2y = 13.50 - 7.50
2y = 6.00
y = 6.00 / 2
y = 3.00
Since the equation holds true, statement A ("Each hot dog costs 2.50") is true.
B. Similarly, to determine if the statement "Each cup of soda costs 3.50" is true, we can use the same equation and substitute the value of y = 3.50:
3x + 2(3.50) = 13.50
3x + 7.00 = 13.50
3x = 13.50 - 7.00
3x = 6.50
x = 6.50 / 3
x = 2.17 (rounded to 2 decimal places)
Since the equation does not hold true when y = 3.50, statement B is not true. Therefore, we can conclude that statement A is true, but statement B is false.
C. The equation 3x + 2y = 13.50 correctly models the total cost of 3 hot dogs and 2 cups of soda, as we derived it previously. So statement C is true.
D. The total cost of 2 hot dogs and 1 cup of soda can be determined by another equation. Let's set up an equation using the given information:
2x + y = 8
This equation correctly models the total cost of 2 hot dogs and 1 cup of soda. So, statement D is true.
In summary, the true statements about this situation are:
A. Each hot dog costs 2.50
C. The total cost of 3 hot dogs and 2 cups of soda can be modeled by the equation 3x + 2y = 13.50
D. The total cost of 2 hot dogs and 1 cup of soda can be modeled by the equation 2x + y = 8