Roman has $40 to spend on snacks for his camping trip. He plans to buy protein bars that cost $3
each and individual bags of trail mix that cost $2 each.
If a represents the number of protein bars that Roman buys and y represents the number of individua bags of trail mix that Roman buys, then which equations represent this situation?
Choose 2.
A. y=-3/2x+20
B. 2x+3y=40
C. y=-2/3x+40/3
D. y=-2/3x+20
E. 3x+2y=40
F. y=3/2x+20
The price of each protein bar is $3 and the price of each trail mix bag is $2.
If Roman buys a number of protein bars represented by x and a number of trail mix bags represented by y, then the total cost of protein bars will be 3x and the total cost of trail mix bags will be 2y.
Since Roman has $40 to spend, the equation representing the total cost is:
3x + 2y = 40.
Therefore, the equation 3x + 2y = 40 represents the situation.
The equation y = -3/2x + 20 does not represent the situation because it does not take into consideration the fact that the total cost is $40.
The equation 2x + 3y = 40 also does not represent the situation because it does not correctly account for the prices of the protein bars and trail mix bags.
Therefore, the correct equations that represent the situation are:
B. 3x + 2y = 40
E. y = -2/3x + 20
The equations that represent this situation are:
B. 2x + 3y = 40
E. 3x + 2y = 40
To find the equations that represent the situation, we need to analyze the given information.
We know that the cost of each protein bar is $3, and Roman plans to buy "a" protein bars. So, the total cost of protein bars would be 3a dollars.
Similarly, the cost of each bag of trail mix is $2, and Roman plans to buy "y" bags of trail mix. So, the total cost of bags of trail mix would be 2y dollars.
Since Roman has a total budget of $40, we can set up the equation:
3a + 2y = 40
This equation represents the total cost of snacks purchased.
Now, let's analyze the given options:
A. y = -3/2x + 20
This equation is not valid because it has terms with "x" and "y", whereas we only have "a" and "y" in the problem.
B. 2x + 3y = 40
This equation is valid as it represents the total cost of the snacks purchased.
C. y = -2/3x + 40/3
This equation is similar to option A and is not valid for the same reason.
D. y = -2/3x + 20
This equation is not valid as it has terms with "x" and "y".
E. 3x + 2y = 40
This equation is valid as it represents the total cost of the snacks purchased.
F. y = 3/2x + 20
This equation is not valid as it has terms with "x" and "y".
The valid equations that represent the situation are B. 2x + 3y = 40 and E. 3x + 2y = 40.