your team is winning 27-18. The announcer says they have scored five times on field goals and touchdowns and haven't missed a point-after-touchdown yet. Can you tell how many touchdowns and field goals your team has made?
+130478 your team is winning 27-18. The announcer says they have scored five times on field goals and touchdowns and haven't missed a point-after-touchdown yet. Can you tell how many touchdowns and field goals your team has made?
Let x be the number of TDs they have scored and let y be the number of field goals they have scored.
Then x + y = 5
And the number of TDs (x) times the point value for each (plus the pt after), i.e., (7) = 7x
And the number of FGs times their point value each = 3y
So the number of total points they have scored is given by
7x + 3y = 27
So we have two equations here
7x + 3y = 27
x + y = 5
Let's solve this system...Using the second equation and subtracting x from both sides, we have y = 5 - x
Now, substituting for y in the first equation, we have
7x + 3(5 - x) = 27 Simplifying, we have
7x + 15 - 3x = 27
4x + 15 = 27 Subtract 15 from both sides
4x = 12 Divide both sides by 3
x = 3.......This is the number of TDs
and the number of field goals (y) is given by 5 - x = 5 - 3 = 2
That makes sense......... 3 TDs and 2 FGs = 21 + 6 = 27
