Answer:
The different ways a football team cold score 63 points are by having;
1) 3 touchdowns and 14 field goals
2) 6 touchdowns and 7 field goals
Step-by-step explanation:
The given parameters are;
The worth of each touchdown = 7 point
The worth of each field goal = 3 points
The number of touch down ≥ 1
The number of field goals ≥ 1
Let x represent the number of touchdowns and let y represent the number of field goals, we have;
7·x + 3·y = 63...(1)
x + y ≥ 2...(1)
Making y the subject of the equation, 7·x + 3·y = 63, gives;
3·y = 63 - 7·x
y = 21 - (7/3)·x
Making y the subject of the inequality, x + y ≥ 2, gives;
y ≥ 2 - x
From the attached graph created with Microsoft Excel, we have the points where x ≥ 1, that have a whole number value of y ≥ 0 as follows;
1) When x = 3, y = 14 gives 7×3 + 3×14 = 63
2) When x = 6, y = 7 gives 7×6 + 3×7 = 63
Therefore, the different ways a football team cold score 63 points are;
1) 3 touchdowns and 14 field goals
2) 6 touchdowns and 7 field goals.
