HELP! Please...

Question

In Super Bowl I, on January 15, 1967, the Green Bay Packers defeated the Kansas City Chiefs by a score of 15 to 30 . The total points scored came from 13 different scoring plays, which were a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3 points, respectively. The same number of touchdowns and extra-point kicks were scored. There were six times as many touchdowns as field goals. How many touchdowns, extra-point kicks, and field goals were scored during the game?

Answer 1

Whew, Nakia, this looks complicated, but we can get through it!  We can look at this and figure it out rather simply actually!

 

Since the same amount of touchdowns and extra points were the same, we'll give them the same variable, x.

 

The number of field goals was 1/6 of the number of touchdowns, so there were (1/6)x field goals.

 

We can combine the touchdowns and extra points into 7 total points for both.  If they scored 2 touchdowns and extra points, then they scored 7 x 2 = 14 points.  Because they scored x touchdowns and extra points, they scored 7x total points.

 

The same goes with the field goals.  The total points on field goals is 3(1/6)x = (1/2)x.

 

45 total points were scored.  7x + (1/2)x = 45.  (7 1/2)x = 45, so x = 6.

 

This means there were 6 touchdowns, 6 extra points, and only 1 field goal.

 

Hope this helps!