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 individual bags of trail mix that Roman buys, then which equations [present this situation?
Choose 2.
A. y = -3/2 + 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 equations that represent this situation are:
B. 2x + 3y = 40
E. 3x + 2y = 40
The correct equations that represent the situation are:
B. 2x + 3y = 40
E. 3x + 2y = 40
Explanation:
Let x represent the number of protein bars and y represent the number of individual bags of trail mix bought.
The cost of the protein bars is $3 each, so the cost of x protein bars is 3x.
The cost of the individual bags of trail mix is $2 each, so the cost of y bags of trail mix is 2y.
Since Roman has $40 to spend, the first equation can be derived as:
3x + 2y = 40
Also, since Roman can buy any number of protein bars and bags of trail mix, he can also buy 0 of either. Therefore, the equation representing this scenario can be derived as:
2x + 3y = 40
Hence, the correct equations are B. 2x + 3y = 40 and E. 3x + 2y = 40.
To determine the equations that represent the situation described, we need to consider the cost of the items Roman plans to purchase.
Let's assume Roman buys 'a' protein bars and 'y' bags of trail mix.
The cost of the protein bars would be 3 * a.
The cost of the trail mix bags would be 2 * y.
Since Roman has $40 to spend, the equation representing the total cost of his purchases can be written as:
3 * a + 2 * y = 40.
Looking at the given options, we can identify that the equation 2x + 3y = 40 matches the equation above, so option B is correct.
Now let's consider the other equation. Since Roman has $40 to spend, the equation representing the total cost can also be written as:
3 * a + 2 * y = 40.
Rearranging the equation, we have:
2 * y = 40 - 3 * a,
Dividing both sides by 2:
y = (40 - 3 * a) / 2.
Simplifying further, we get:
y = -3a/2 + 20.
Thus, the equation y = -3/2 * a + 20 represents the situation as well.
Therefore, the correct options are B. 2x + 3y = 40 and F. y = -3/2a + 20.