Question

2. In 2005 the UT Longhorns scored 15 times to win the Big 12 Championship Game 70-3. All of

their points came from touchdowns (6 points each) and extra point kicks (1 point each). How

many touchdowns and extra points did the Longhorns have in that game? (For the purposes of

this problem, touchdowns and extra point kicks count as separate "scores".

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Answer 1

Answer: 11 touchdowns and 4 extra points kicks.

Explanation:

They scored 15 times to get 70 points

The easiest way to approach this problem is to make assumptions and see by substitution if the assumptions holds.

1) We need to know the least touchdowns they have to score

2) The number of extra points kicks left to give us the exact 70 points

3) the summation of (1) and (2) must be 15

The first assumption will be to know the number of possible touchdowns in 70 points.

That is; 70/6 = 11.666

✓ Let's assume it's 11 touchdowns.

11× 6 = 66 points (they touchdowns 11 times)

✓ We need 4 more points to get 70 points

✓ Let's assume 4 touchdowns,

4×1 = 4 points

66 + 4 = 70 points

This means that 11 touchdowns + 4 extra points kicks will mean they scored 15 times.

There is a small note addition, to help and support the answer as correct. Thanks.

Answer 2

11 touchdowns and 4 extra point kicks

Explanation:

First, the corresponding system of equations must be considered. In this case we have two unknowns (Touchdowns and extra point kicks) and we know beforehand the number of annotations and the number of points made. According to the above we can propose the following system of equations:

`\left \{ {{x+y=15} \atop {6x+y=70}} \right.`

Where

x are the number of touchdowns

y are the number of extra point kicks.

You can use various methods of system resolution. In this case I will use the replacement method. The idea is to put an unknown in the other equation. Since the first equation is simpler, we will isolate x in it in this way.

`x=15-y`

Then we enter the above into the second equation like this:

`6(15-y)+y=70`

`90-6y+y=70`

`5y=20` We leave the unknowns aside and the rest on the other.

`y=4` Now we know the number of extra point kicks , which we enter in the third equation we made.

`x=15-4`

`x=11` Now we know the number of touchdowns