n represent the number of games lost, write an equation for:
a) A team won three times as many games as it lost. It played a total of 52 years.
b) A team won 20 games more than it lost. It played a total of 84 games.
c) A team won 15 games less than twice the number lost. It played a total of 78 games.
Thank you.
Assuming "years" means "games," the first equation will be:
n + 3n = 52
With this solution, you should be able to generalize to provide the rremaining two equations.
I hope this helps. Thanks for asking.
Sure! Let's solve these problems one by one and write the equations for each scenario:
a) A team won three times as many games as it lost. It played a total of 52 games.
Let's denote the number of games lost as "n". According to the given information, the number of games won is three times the number of games lost. So, we can write the equation as:
Games won = 3 * Games lost
Since the team played a total of 52 games, we can also write the equation as:
Games won + Games lost = 52
Combining both equations, we get:
3 * Games lost + Games lost = 52
Simplifying the equation, we have:
4 * Games lost = 52
Dividing both sides of the equation by 4, we get:
Games lost = 13
Therefore, the equation for scenario (a) is Games lost = 13.
b) A team won 20 games more than it lost. It played a total of 84 games.
Again, let's denote the number of games lost as "n". According to the given information, the number of games won is 20 more than the number of games lost. So, we can write the equation as:
Games won = Games lost + 20
Since the team played a total of 84 games, we can also write the equation as:
Games won + Games lost = 84
Combining both equations, we get:
Games lost + 20 + Games lost = 84
Simplifying the equation, we have:
2 * Games lost = 64
Dividing both sides of the equation by 2, we get:
Games lost = 32
Therefore, the equation for scenario (b) is Games lost = 32.
c) A team won 15 games less than twice the number lost. It played a total of 78 games.
Once again, let's denote the number of games lost as "n". According to the given information, the number of games won is 15 less than twice the number of games lost. So, we can write the equation as:
Games won = 2 * Games lost - 15
Since the team played a total of 78 games, we can also write the equation as:
Games won + Games lost = 78
Combining both equations, we get:
2 * Games lost - 15 + Games lost = 78
Simplifying the equation, we have:
3 * Games lost = 93
Dividing both sides of the equation by 3, we get:
Games lost = 31
Therefore, the equation for scenario (c) is Games lost = 31.
I hope this helps! If you have any more questions, feel free to ask.