Question

During their last game, the Miami Dolphins scored ͸ times for a total score of ͵Ͳ points. They scored ͹ points for each touchdown and ͵ points for each field goal. Write and solve the systems of equations to find the total touchdowns and field goals scored.

Answer 1

The Miami Dolphins had 3 touchdowns and 3 field goals.

Explanation:

It is given that During their last game, the Miami Dolphins scored 6 times, for a total score of 30 points. They scored 7 points for each touchdown and 3 points for each field goal.

We need to write and solve the system of equations to find the total touchdowns and field goals scored.

Let x represents the number of touchdowns.

Let y be the number of field goals.

It is given that the Miami Dolphins scored 6 times

`x+y=6`

`x=6-y`....(1)

They scored 7 points for each touchdown and 3 points for each field goal.

The total score is 30 points:

`7x+3y=30` ...(2)

Put the value of x from equation (1) into equation (2).

`7( 6-y)+3y=30`

`42-7y+3y=30`

`-4y=30-42`

`-4y=-12`

`y=3`

Put y = 3 in equation 1.

`x=6-3`

`x=3`

Hence, the Miami Dolphins had 3 touchdowns and 3 field goals.