Question

A high school football team scored 39 points in the game last night, with a combination of touchdowns (6 points each), extra points (1 point each), and field goals (3 points each).
The team make 1 more extra point than field goals, represented by the equation e=f+1, where e is the number of extra points and f is the number of field points scored.
They also scored five times as many points on touchdowns as field goals, represented by the equation 6t=15f, where t is the number of touchdowns and f is the number of field goals scored.
Write a system of equations representing this situation and use it to complete the statement.
The team scored __ touchdowns, __ extra points, and __ field goals.

Answer 1

Answer:

39=6t+3f+e

39=19f+1

5 touchdowns, 3 extra points, and 2 field goals.

Step-by-step explanation:

e=f+1

6t=15f

39= 6t   +3f   +e

       ^       ^      ^

39=(15f)+(3f)+(f+1)           |             e=f+1                     |                      6t=15f

39=19f+1                         |             e=2+1                    |                      6t=15(2)

38=19f                            |             e=3                        |                      6t=30

f=2                                  |                                            |                      t=5