Question

In football, a field goal counts 3 points and extra points after touchdowns count as 1 point. A kicker scores 30 points on 16 kicks.

How many of the kicks are field goals?

Answer 1

Here we need to set up a system of equations.
Let f = field goal and let e = extra point
f+e=16
3f+1e=30
The first equation tells us that he kicked 16 kicks composed of field goals and extra points.
The second equation tells us that 1 field goal is worth 3 points, one extra point is worth 1 point, and the total point scored was 30.
Now that we have this system of equations do you know how to solve it? You could use substitution, elimination, or graphing.
Let me know if you get stuck. :)

Answer 2

I'm lost..

Answer 3

Hmm..ok.
The first equation tells us the number of each field goal/extra points he kicked. Since we don't know how many field goals or extra points he kicked, we represent these as unknowns. (f and e) We do know that he kicked a total of 16 kicks composed of field goals and extra points though, so we can set up the first equation.
f+e=16 ---or (number or field goals) + (number of extra points) = 16 total kicks
The second equation tells us the vales of the field goals and extra kicks. It said that a field goal was worth 3 points and an extra point was worth 1 point. We also know that he got a total of 30 points in the game.
Now we can set up our second equation.
3f+1e=30 ---or (value of field goals)(number of field goals) + (value of extra points)(number of extra points) = total value of field goals and extra points.

Now that we have these two equations, we can solve them to figure out how many kicks were field goals.
Does this make any sense? Sorry, I'm probably just confusing you more....

Answer 4

little.. mostly confused...

Answer 5

Sorry for the confusion. :/
I'll just finish showing you how you would solve this...maybe it will come full circle and you'll understand or something..

Now that we have the two equations, we can solve with a graphing, elimination, or substitution. I'll show you how to do it with elimintation.
f+e=16
3f+1e=30

We can multiply everything in the first equation by a minus, so now we have:
-f-e=-16

And now we can "add" this to the other equation, e will cancel, and we can solve for f (which is the number of field goals he kicked.)
-f -e=-16
+3f +e= 30
--------------
2f = 14
f = 7

So he kicked 7 field goals.

If we want to figure out how many extra points he scored, we can put 7 in where f was in out first equation (becuase f = 7) and it will tell us how many extra points he scored.
f+e=16
(7)+e = 16
e = 9

So he kicked 7 field goals and 9 extra points.

Now let's put the values of e and f in our second equation.
3f+1e=30
3(7)+1(9)=30
21+9=30
30 = 30.

So this is how you would check it.
If you think about it, this makes sense. He kicked 7 field goals worth 3 points, and he kicked 9 extra points worth 1 point, and got a total of 30 points.
He did get 30 points, so it works.


Again, sorry if this just further confuses you. I'm not really the best at explaining this kind of stuff. :/

Answer 6

OH! I understand now, thank you!

Answer 7

Really?
Ok, cool. I'm glad it clicked for you.
And your welcome! I'm glad you could figure it out.