# Directions: Define 2 variables, write 2 equations, and solve the system of equations. The North Ridgeville Football team played a game against Avon last week. A total of 125 points were scored by both teams. The teams scored a total of 22 six-point touchdowns and three-point field goals. In additon, there were 4 two-point safeties and 12 one-point kids scored. How many touchdowns and field goals were scored by the teams during the game?

Question
Equations
Directions: Define 2 variables, write 2 equations, and solve the system of equations.
The North Ridgeville Football team played a game against Avon last week. A total of 125 points were scored by both teams. The teams scored a total of 22 six-point touchdowns and three-point field goals. In additon, there were 4 two-point safeties and 12 one-point kids scored. How many touchdowns and field goals were scored by the teams during the game?

2020-11-09
Step 1
Let x and y denote the number of touchdowns and field goals were scored by the teams during the game.
Given that:
Total touchdowns and field goals scored = 22
x + y = 22
Total score = Total scores of touchdowns, field goals and additional points, that is,
$$\displaystyle{125}={6}{x}+{3}{y}+{4}\times{2}+{12}\times{1}$$
$$\displaystyle\Rightarrow{6}{x}+{3}{y}={105}$$
$$\displaystyle\Rightarrow{2}{x}+{y}={35}$$
Step 2
Therefore, the system of equations to solve is:
x+y=22
2x+y=35
First, eliminate y.
Subtract first equation from the second equation to get
x = 13
Step 3
Solve for y by substituting the value for x in either of the two equations:
$$\displaystyle{13}+{y}={22}\Rightarrow{y}={9}$$
Thus, 13 touchdowns and 9 field goals were scored by the teams.

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