Define a variable and write an inequality. Then solve. A local summer baseball team plays 20 games each season. So far, they have won 9 games and lost 2. How many more games must they win this season to win at least 75% of all their games?
I don't know what define a variable means but here is my work
9 + 2 <= 20
they must win 6 more games
A variable can be a symbol or word used to represent some value. For this problem W could be a variable representing the number of additional games that they must win to have won 75%.
(number won so far) + (addtional won) >= 75% (total games)
substituting...
9 + W >= 0.75 * (20)
Solve for W
If they win n more games then
total games won = 9+n
(9+n)/20 >/=.75
9+n >/= 15
n>/= 6
To solve this problem, we need to define a variable and write an inequality.
Let's define a variable, "x", to represent the number of additional games the team needs to win this season to achieve their goal.
The inequality we can write is:
(9 + x) / (20 + x) ≥ 0.75
In this inequality, the numerator represents the number of games the team has already won, while the denominator represents the total number of games played (including the additional games they need to win).
To solve this inequality, we can start by getting rid of the fraction by multiplying both sides of the inequality by (20 + x):
(9 + x) ≥ 0.75 * (20 + x)
Distribute the 0.75 to both terms on the right side of the inequality:
9 + x ≥ 0.75 * 20 + 0.75 * x
Simplify the equation by multiplying:
9 + x ≥ 15 + 0.75x
Next, we want to isolate the variable terms on one side of the inequality, so we subtract 0.75x from both sides:
9 + x - 0.75x ≥ 15 + 0.75x - 0.75x
Combine like terms:
0.25x + 9 ≥ 15
Subtract 9 from both sides:
0.25x + 9 - 9 ≥ 15 - 9
Simplify the equation:
0.25x ≥ 6
To isolate the x, we divide both sides of the inequality by 0.25:
(0.25x) / 0.25 ≥ 6 / 0.25
Simplify the equation:
x ≥ 24
Therefore, the team must win at least 24 more games this season to win a minimum of 75% of all their games.