The best sports dorm on campus, Lombardi House, has won a total of 7 games this semester. Some of these games were soccer games, and the others were football games. According to the rules of the university, each win in a soccer gamer earns the winning house 3 points, whereas each win in a football game earns them 7 points. If the total number of points Lombardi House earned was 41, how many of each type of game did they win ?
A)5 soccer games and 2 football games
B) 3 soccer games and 4 football games
C) 2 soccer games and 5 football games
D) 0 soccer games and 7 football games
E) 7 soccer games and 0 football games

Question

The best sports dorm on campus, Lombardi House, has won a total of 7 games this semester. Some of these games were soccer games, and the others were football games. According to the rules of the university, each win in a soccer gamer earns the winning house 3 points, whereas each win in a football game earns them 7 points. If the total number of points Lombardi House earned was 41, how many of each type of game did they win  ?
A)5 soccer games and 2 football games
B) 3 soccer games and 4 football games
C) 2 soccer games and 5 football games
D) 0 soccer games and 7 football games
E) 7 soccer games and 0 football games

Quizplus · Accepted Answer

Let's denote the number of soccer and football games won by x and y respectively. Therefore, we have two equations: 
3x + 7y = 41 (total point system)
x + y = 7 (total number of games)
Now we can use substitution to solve for x and y. Rearranging the second equation, we get x = 7 - y. Substituting this into the first equation, we get 3(7-y) + 7y = 41. Simplifying this equation gives us y = 5. Substituting y = 5 back into x = 7-y gives us x = 2. Therefore, Lombardi House won 2 soccer games and 5 football games.

The Best Sports Dorm on Campus, Lombardi House, Has Won