The inequality 10x + 20y > 500 models all of the combinations of scores of 10 and 20 points that will give a total greater than 500 points in a game. What is not true about the values for x and y?
they are not integers
they may be negative
To determine what is not true about the values for x and y in the inequality 10x + 20y > 500, we need to analyze the equation.
The inequality represents all the combinations of scores (x and y) that will result in a total greater than 500 points in a game. Let's break it down:
10x represents the score obtained by multiplying 10 points by the variable x.
20y represents the score obtained by multiplying 20 points by the variable y.
Since we want the total score (10x + 20y) to be greater than 500, we can solve the inequality by applying algebraic operations:
10x + 20y > 500
Subtract 10x from both sides:
20y > 500 - 10x
Divide both sides by 20:
y > (500 - 10x) / 20
Simplifying further:
y > 25 - 0.5x
Now, let's consider the factors involved:
1. The value of y cannot be less than 25 - 0.5x. In other words, y must be greater than the expression (25 - 0.5x). This holds true because the inequality is strict, implying that only values greater than (25 - 0.5x) satisfy the equation.
2. The value of x is not restricted by the equation. Since y depends on x in the expression (25 - 0.5x), varying x will alter the lower bound for y but not the upper bound. Therefore, any real value can be chosen for x.
In conclusion, what is not true about the values for x and y is that x is not restricted, while y needs to be greater than (25 - 0.5x) to satisfy the inequality.