Create video explaining how to solve this problem---**Question Stem:**
Cameron took 4 tests, and his scores were as follows: 100, 60, 80, and 30. Cameron took another test that was scored x. The mean score of the 5 tests he took is 72. What is the value of x?
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Let's solve this step by step. Cameron took 4 tests with scores of 100, 60, 80, and 30. He then took a fifth test that received a score of x. We're told that the mean score of all 5 tests is 72, and we need to find the value of x.
To solve this problem, we need to understand the mean formula. The mean equals the sum of all values divided by the number of values. For Cameron's situation, we have 5 tests total, and we know the mean is 72. So we can write the equation: 72 equals the sum of 100, 60, 80, 30, and x, all divided by 5. This gives us an equation we can solve for x.
Now let's set up our equation step by step. We start with 72 equals the sum of 100, 60, 80, 30, and x, all divided by 5. First, we'll add up the known test scores: 100 plus 60 plus 80 plus 30 equals 270. Now we can rewrite our equation as 72 equals 270 plus x, all divided by 5. This gives us a much simpler equation to work with.
Now let's solve for x step by step. Starting with 72 equals 270 plus x, all divided by 5. First, we multiply both sides by 5 to eliminate the fraction. This gives us 72 times 5 equals 270 plus x, which simplifies to 360 equals 270 plus x. Next, we subtract 270 from both sides to isolate x. This gives us 360 minus 270 equals x, so x equals 90. Therefore, Cameron's fifth test score was 90.
Let's verify our answer by substituting x equals 90 back into the original problem. The mean of all five test scores should be 72. We calculate: 100 plus 60 plus 80 plus 30 plus 90, all divided by 5. This equals 360 divided by 5, which equals 72. Perfect! This confirms our answer is correct. To summarize our solution process: we identified the known values, set up the mean equation, solved it algebraically, and verified our solution. The value of x is 90.