Question

A kicker on a football team scores 1 point for making an extra point and 3 points for making a field goal. The kicker makes a total of 6 extra points and field goals and scores 12 points. Write and solve a system of equations to find the number of extra points and field goals.

Answer 1

The kicker made 4.5 extra points and 1.5 field goals.

Step-by-step explanation:

Let's define the variables:

x = number of extra points

y = number of field goals

According to the problem, the kicker scored a total of 6 extra points and field goals and scored 12 points:

1. Equation 1: x + y = 6
2. Equation 2: 1x + 3y = 12

We can then solve this system of equations using substitution or elimination:

Using substitution:

1. Equation 1: x = 6 - y
2. Substitute equation 1 into equation 2: 1(6 - y) + 3y = 12
3. Simplify and solve for y: 6 - y + 3y = 12 → 4y = 6 → y = 1.5
4. Substitute y = 1.5 into equation 1 to find x: x = 6 - 1.5 = 4.5

Final answer: The kicker made 4.5 extra points and 1.5 field goals.