a minor league baseball team plays 88 games in a season . if the team won 17 more then twice as many games as they lost , how many wins and losses did the team have
X = Games lost
(2X + 17) = Games won.
X + ( 2X +17 ) = 88
Solve for x:
X = 23.7 = 24 Games lost
2X + 17 = 2(24) + 17 = 65 Games won.
Maybe the number of games played
should be 89. check it out.
To solve this problem, let's break it down into steps:
Step 1: Assign variables.
Let's assign the variable "x" to represent the number of games the team lost.
Since the team won 17 more than twice the number of games they lost, the number of games they won can be represented as (2x + 17).
Step 2: Create an equation.
The total number of games played in the season is 88, so the sum of wins and losses should be equal to 88. We can write this as:
x + (2x + 17) = 88
Step 3: Simplify and solve the equation.
Combine like terms:
3x + 17 = 88
Subtract 17 from both sides of the equation:
3x = 71
Divide both sides by 3:
x = 71 / 3
x is not a whole number, which doesn't make sense in the context of this problem. The number of games lost cannot be a fraction. Therefore, the assumption we made at the beginning must be incorrect.
Let's go back to Step 1 and reassess our initial assumption.
Instead of using x to represent the number of games lost, let's use x to represent the number of games won. Therefore, the number of games lost can be represented as (2x + 17).
Step 2: Create an equation.
Using the new assignments, we can write the equation as:
(2x + 17) + x = 88
Step 3: Simplify and solve the equation.
Combine like terms:
3x + 17 = 88
Subtract 17 from both sides of the equation:
3x = 71
Divide both sides by 3:
x = 71 / 3
x is approximately 23.67.
Since the team cannot win a fraction of a game, we need to round this number down to the nearest whole number. Therefore, x ≈ 23.
Now that we have found the value of x, we can substitute it back into the equation to find the number of games lost:
2x + 17 = 2(23) + 17 = 63.
So, the team won approximately 23 games and lost 63 games.