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

39=6t+3f+e

39=19f+1

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

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