To set up the inequality for the situation, we need to account for the points scored from successful point-after tries (PATs) and field goals:
- Each successful point-after try contributes 1 point (let \( x \) be the number of successful PATs).
- Each successful field goal contributes 3 points (let \( y \) be the number of field goals).
Given that Adam Vinatieri had 2253 total points at the beginning of the 2016 season, we want to determine how many successful PATs and field goals he could achieve in order to surpass Morten Andersen's record of 2544 total points.
The inequality representing the requirement to surpass Andersen's record is:
\[ 2253 + 1x + 3y > 2544 \]
Subtracting 2253 from both sides gives:
\[ 1x + 3y > 291 \]
Now, we can express this in the standard form \( Ax + By + C > 0 \):
\[ x + 3y - 291 > 0 \]
This can also be written as:
\[ x + 3y + (-291) > 0 \]
To make it clearer, we can represent the standard form as follows:
\[ 1x + 3y - 291 > 0 \]
Thus, the required components of the inequality in standard form are:
- A: 1 (coefficient of \( x \))
- B: 3 (coefficient of \( y \))
- C: -291
- In the form \( x + By > C \), we have:
\[ x + 3y > 291 \]
So the final answers are:
- ___x = 1
- ___y = 3
- ___C = -291
And for the simplified form:
- \( x + ___y = 291 \); thus, this is \( x + 3y > 291 \).
1, 3, and -291 for the respective boxes.