Question 1
Write a one-step equation that relates the number of x
enemies defeated to the maximum high score.
Question 2
Solve the equation to find how many enemies would need to be defeated to achieve the high score.
Your friend suggests that the player should get a fixed amount of bonus points for completing a level. You agree and suggest 200 points for completing the first level.
Question 3
Write a two-step equation that represents how to calculate the player’s high score.
Question 4
Solve the equation to find out how many enemies need to be defeated now to reach the high score.
You suggest that, to make the next level harder, the points awarded for enemies should be higher but the completion bonus lower. You set the enemy points to 60 and the completion bonus to 100 while keeping the maximum score at 1,000. You wonder whether it is possible to defeat the same number of enemies in each level and get the same score.
Question 5
Write an equation that sets the expression for the score of the first level equal to the one for the second level score.
Question 6
How many enemies would you have to defeat in both levels to achieve the same score?
Question 7
What is the score in each level when that number of enemies is defeated?
Question 1:
Let's say the number of enemies defeated is represented by 'x' and the maximum high score is represented by 'y'. The equation that relates these two variables is:
y = 50x
Question 2:
If the maximum high score is 1000, then we can solve for x by substituting in the value of y:
1000 = 50x
x = 20
Therefore, the player would need to defeat 20 enemies to achieve the high score.
Question 3:
Let's denote the number of enemies defeated as 'x', the completion bonus as 200, and the points awarded for enemies as 60. The equation for calculating the player's high score would be:
y = 60x + 200
Question 4:
If the maximum high score is 1000, then we can solve for x by substituting in the value of y:
1000 = 60x + 200
800 = 60x
x = 13.33
Therefore, the player would need to defeat 14 enemies to achieve the high score.
Question 5:
Let's denote the number of enemies defeated in the first level as 'a' and in the second level as 'b'. The equation that sets the expression for the score of the first level equal to the one for the second level score is:
60a + 100 = 50b + 100
Question 6:
To find out how many enemies need to be defeated in both levels to achieve the same score, we can solve the equation:
60a + 100 = 50b + 100
60a = 50b
a = 5/6 * b
Therefore, the player would need to defeat 5/6 times the number of enemies in the second level to achieve the same score.
Question 7:
If we plug in the value of 'a' in terms of 'b':
60(5/6 * b) + 100 = 50b + 100
50b + 100 = 50b + 100
100 = 100
Therefore, the score in each level when that number of enemies is defeated would be 100.