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".

The number of touch downs = 11

The number of extra points = 4

Step-by-step explanation:

The number of times UT Longhorns scored = 15 times

The composition of the scores = Touch down and point kicks

The points with which UT Longhorns won the game = 70-3

The points that came from each touch down = 6 points

The points that came from each point kick = 1 points

We have;

The number of touch downs + Point kicks = 15

The number of touch downs = 15 - Point kicks

Let the number of point kicks = P

Therefore;

The number of touch downs = 15 - Point kicks = 15 - P

The number of touch downs = 15 - P

Given that the total points of UT Longhorns = 70, we have;

6 × (15 - P) + 1 × P = 70

90 - 6·P + P = 70

5·P = 90 - 70 = 20

P = 4

∴ The number of point kicks = P = 4

The number of point kicks, extra points = 4

The number of touch downs = 15 - P = 15 - 4 = 11

The number of touch downs = 11

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

i hope this is what you were looking for.

see attached graph