Question

1. a football team scored twice as many points off of 3 point field goals as they scored touchdowns worth 6 points. knowing they scored a total of 36 points from field goals and touchdowns, how many field goals were made and how many touchdowns were scored?

the team made -- choose the correct answer -- field goals and scored -- choose the correct answer -- touchdowns.

clear all

Explanation:

Step1: Define Variables

Let \( x \) be the number of touchdowns (each worth 6 points, so total touchdown points: \( 6x \)). Let \( y \) be the number of field goals (each worth 3 points, so total field goal points: \( 3y \)).

Step2: Set Up Equations

From "twice as many points off field goals as touchdowns": \( 3y = 2(6x) \) → \( 3y = 12x \) → Simplify: \( y = 4x \).
From total points: \( 6x + 3y = 36 \).

Step3: Substitute \( y = 4x \) into Total Points Equation

Substitute \( y = 4x \) into \( 6x + 3y = 36 \):
\( 6x + 3(4x) = 36 \) → \( 6x + 12x = 36 \) → \( 18x = 36 \) → \( x = 2 \) (touchdowns).

Step4: Find \( y \) (Field Goals)

Substitute \( x = 2 \) into \( y = 4x \): \( y = 4(2) = 8 \) (field goals).

Answer:

The team made 8 field goals and scored 2 touchdowns.