the highest test score scott can receive is a 100.The sum of his first four test scores is atleast 360.Find the range of scores scott must get on his fifth test to have an average greaterthan 70?
(360+S)/5=70 so
S=360-350 which means he can get as low as -10 and get a 70 average. Now his teacher may not give minus scores, so he can score zero to 100 and get his 70 average.
To find the range of scores Scott must get on his fifth test to have an average greater than 70, we need to determine the minimum and maximum values for his fifth test score.
Let's start by finding the minimum possible score for Scott's fifth test. To do this, we will assume that Scott's first four test scores are at their minimum allowed values. Since the sum of his first four test scores is at least 360, we can set up the following inequality:
x + y + z + w ≥ 360
where x, y, z, and w represent Scott's first four test scores, and w is his fifth test score.
Now, we know that the highest possible test score Scott can receive is 100. So, to find the minimum value for w, we can assume the other four test scores (x, y, z) are at their minimums and solve for w:
x + y + z + 100 ≥ 360
Simplifying, we have:
x + y + z ≥ 260
Since we are looking for Scott's average to be greater than 70, we can divide both sides of the equation by 4:
(x + y + z) / 4 ≥ 70
Now, let's find the maximum possible score for Scott's fifth test. To do this, we will assume that Scott's first four test scores are at their maximum allowed values. Since the sum of his first four test scores is at least 360, we can set up the following inequality:
x + y + z + w ≥ 360
where x, y, z, and w represent Scott's first four test scores, and w is his fifth test score.
Since the highest possible test score Scott can receive is 100, we can set up the inequality:
100 + 100 + 100 + 100 + w ≥ 360
Simplifying, we have:
400 + w ≥ 360
Subtracting 400 from both sides, we get:
w ≥ -40
Since Scott cannot score below 0, we can conclude that the minimum score for his fifth test is 0.
Therefore, the range of scores Scott must get on his fifth test to have an average greater than 70 is 0 to 100.