2. Let the lowest score be x. Then, the highest score would be x+21. We know that the sum of the highest and lowest score is 105, so we can set up the equation:
x + (x+21) = 105
2x + 21 = 105
2x = 84
x = 42
Therefore, the highest score in the distribution is 42+21 = 63.
3. Using the same reasoning as above, we know that the lowest score is x. From part 2, we found that x = 42. Therefore, the lowest score in the distribution is 42.
Answers & Comments
Answer:
To solve this problem, we can use a system of two equations with two variables.
Let's assume that the highest score in the distribution is represented by "x" and the lowest score is represented by "y". We know that:
The range of the distribution is 21. This means that x - y = 21.
The sum of the highest and lowest scores is 105. This means that x + y = 105.
Now we can solve for x and y by solving the system of equations:
x - y = 21 (equation 1)
x + y = 105 (equation 2)
Adding equations 1 and 2, we get:
2x = 126
Dividing both sides by 2, we get:
x = 63
Substituting x = 63 into equation 2, we get:
63 + y = 105
Subtracting 63 from both sides, we get:
y = 42
Therefore, the highest score in the distribution is 63 and the lowest score is 42.
Answer:
2. Let the lowest score be x. Then, the highest score would be x+21. We know that the sum of the highest and lowest score is 105, so we can set up the equation:
x + (x+21) = 105
2x + 21 = 105
2x = 84
x = 42
Therefore, the highest score in the distribution is 42+21 = 63.
3. Using the same reasoning as above, we know that the lowest score is x. From part 2, we found that x = 42. Therefore, the lowest score in the distribution is 42.