Mike took four tests: English, Math, Science and History. He scored a 74 in English and an 84 in History. The average of the four tests was 72. Math had a better score than Science by 6 points. What was his Science score?
English = 74
History = 84
Science = x
Math = x+6
so
(74+84+x+x+6)/4 = 72
solve for x
To find Mike's Science score, let's follow these steps:
Step 1: Calculate the sum of Mike's scores for the four tests.
The average of the four tests is given as 72. Since there are four tests in total, multiplying the average by 4 will give us the sum of the four scores.
Average = Sum of scores / Number of tests
72 = Sum of scores / 4
Multiply both sides of the equation by 4:
72 * 4 = Sum of scores
288 = Sum of scores
Step 2: Determine the score in Math based on the given information.
It is stated that Math had a better score than Science by 6 points. Therefore, we can assume that Mike's Math score is 6 points higher than his Science score.
Math Score = Science Score + 6
Step 3: Substitute the known scores into the sum of scores equation.
Given that Mike scored a 74 in English, an 84 in History, and that his Math score is 6 points higher than his Science score, we can substitute those values into the sum of scores equation.
Sum of scores = English Score + Math Score + Science Score + History Score
= 74 + (Science Score + 6) + Science Score + 84
Simplifying the equation:
288 = 164 + 2 * Science Score
Subtracting 164 from both sides:
288 - 164 = 164 - 164 + 2 * Science Score
124 = 2 * Science Score
Step 4: Solve for Mike's Science score.
Divide both sides of the equation by 2:
Science Score = 124 / 2
Science Score = 62
Therefore, Mike's Science score is 62.