Question

In a football game, Kingston can make a touchdown worth 6 points or a field goal worth 3 points. Kingston scored a total of 15 points. Let x represent the number of touchdowns and y represent the number of field goals. Which equation can be used to model the situation?
Group of answer choices

6x + 3y = 15

3x + 6y = 15

15x − 3y = 6

x + y = 15

Answer 1

Answer: Choice A

6x+3y = 15

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Work Shown:

x = number of touchdowns

y = number of field goals

6x = points only from the touchdowns (ignore the fieldgoals for now)

3y = points only from the field goals (ignore the touchdowns for now)

6x+3y = total number of points from both categories combined

6x+3y = 15 since Kingston scored 15 points overall

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Extra info (optional section)

We don't have enough info to fully nail down what x and y are in terms of numbers, but let's say he scored y = 1 field goal.

Then x would be,

6x+3y = 15

6x+3(1) = 15

6x+3 = 15

6x = 15-3

6x = 12

x = 12/6

x = 2

This tells us that Kingston scored 2 touchdowns if he scored 1 field goal.

2 touchdowns + 1 field goal = 2*6 + 1*3 = 12 + 3 = 15 points total

The ordered pair (x,y) = (2,1) is one solution to that equation.

Another solution is (x,y) = (1,3) following similar steps as shown above.

The third solution is (x,y) = (0,5). Each time x goes down by 1, y goes up by 2 and vice versa.

We only have 3 solutions in this case because x & y are nonnegative whole numbers. If x and/or y were allowed to be any real number, then we'd have infinitely many solutions.