In the Animal Football League, the teams can score only 3-point field goals and 7-point touchdowns; no safeties or extra-credit points are allowed. In one contest, the Anteaters scored 81 points. If they scored 3 more touchdowns than field goals, how many touchdowns and field goals did they score?
A) 18 touchdowns and 15 field goals
B) 10 touchdowns and 7 field goals
C) 8 touchdowns and 5 field goals
D) 9 touchdowns and 6 field goals
E) 9 touchdowns and 12 field goals

Question

In the Animal Football League, the teams can score only 3-point field goals and 7-point touchdowns; no safeties or extra-credit points are allowed. In one contest, the Anteaters scored 81 points. If they scored 3 more touchdowns than field goals, how many touchdowns and field goals did they score? ​
A) 18 touchdowns and 15 field goals
B) 10 touchdowns and 7 field goals
C) 8 touchdowns and 5 field goals
D) 9 touchdowns and 6 field goals
E) 9 touchdowns and 12 field goals

Quizplus · Accepted Answer

Let's assume that the Anteaters scored t touchdowns and f field goals. From the given conditions, we know that:
- Each field goal is worth 3 points
- Each touchdown is worth 7 points
- The total score was 81 points
- The number of touchdowns scored was 3 more than the number of field goals scored.

Using these conditions, we can set up two equations based on the total score and the number of touchdowns and field goals:

3f + 7t = 81    (Total score equation)
t = f + 3        (Touchdown equation)

We can substitute the second equation into the first equation to eliminate t and solve for f:

3f + 7(f + 3) = 81
10f + 21 = 81
10f = 60
f = 6

Now we know that the Anteaters scored 6 field goals. We can use the second equation to find the number of touchdowns:

t = f + 3
t = 6 + 3
t = 9

Therefore, the Anteaters scored 9 touchdowns and 6 field goals, which is choice (D).

In the Animal Football League, the Teams Can Score Only