Merv wants to be a football (American soccer) star. To be scouted by a professional team, she needs to score an average of at least 4 goals per game. Her current stats are 6 goals, 1 goal, no goals, and 3 goals. How many goals does she need to score in her next game to get scouted?
variable
inequality
inverse operation steps - will require multiple steps!
solution with inequality symbol
open or closed circle, arrow pointing left or right
Let's use the variable x to represent the number of goals Merv needs to score in her next game.
To find out how many goals she needs to score in her next game to get scouted, we need to set up an inequality. We know that Merv needs to score an average of at least 4 goals per game, so we can set up the inequality:
[(6 + 1 + 0 + 3 + x) / (4 + 1)] >= 4.
Simplifying the expression on the left side of the inequality:
[10 + x] / 5 >= 4.
Now, let's multiply both sides of the inequality by 5 to get rid of the fraction:
10 + x >= 20.
Next, subtract 10 from both sides of the inequality:
x >= 10.
So, Merv needs to score at least 10 goals in her next game to get scouted.
what circle where it point
The circle in the inequality should be a closed circle (or a solid dot) because the condition includes the equal sign.
arrow pointing left or right?
The arrow in the inequality should be pointing to the right because the inequality states that Merv needs to score "at least" 10 goals, which means the value of x (the number of goals she needs to score) must be greater than or equal to 10.
To determine how many goals Merv needs to score in her next game to get scouted, we can use an inequality. Let's assume she needs to play n more games to be scouted, and she wants her average to be at least 4 goals per game.
We can represent this as an inequality:
(6 + 1 + 0 + 3 + x)/n ≥ 4
Where x represents the number of goals she scores in her next game, and n represents the total number of games she has played so far.
To solve this inequality, we can start by distributing the numerator:
10 + x/n ≥ 4
Next, we can subtract 10 from both sides of the inequality:
x/n ≥ 4 - 10
Simplifying further:
x/n ≥ -6
To eliminate the fraction, we can multiply both sides of the inequality by n:
nx/n ≥ n(-6)
Which simplifies to:
x ≥ -6n
Since Merv wants to be scouted, the number of games she has played so far cannot be 0. Let's assume she has played at least one game (n ≥ 1). In this case, we can assume n is a positive number.
When n is positive, we know that -6n will be a negative number. So, the inequality x ≥ -6n means that the number of goals she needs to score in her next game must be greater than or equal to a negative number.
Therefore, to get scouted, Merv needs to score at least 1 goal in her next game.