2. Risa took her periodical tests on several subjects. Her average score not including her Mathematics score is 87. Her average score including her Mathematics score is 86. If her score in Mathematics is 82, how many periodical tests did she take including that in Mathematics?
[87 (p - 1)] + 82 = 86 p
If there were x in all,
87(x-1)+82 = 86x
To find the number of periodical tests Risa took, including the Mathematics test, we can use the concept of averages.
Let's denote the number of tests Risa took (excluding Mathematics) as 'n'.
We know that Risa's average score without her Mathematics score is 87. This means that the sum of her scores in the other subjects (excluding Mathematics) is 87n.
Similarly, we know that her average score including Mathematics is 86. This means that the sum of all her scores, including Mathematics, is 86 times the total number of tests (including Mathematics).
Since the score in Mathematics is 82, the sum of all her scores (including Mathematics) can be expressed as (87n + 82).
Now, we can set up an equation to solve for 'n':
(87n + 82) / (n + 1) = 86
To solve this equation:
1. Multiply both sides of the equation by (n + 1) to eliminate the denominator:
87n + 82 = 86(n + 1)
2. Distribute on the right side of the equation:
87n + 82 = 86n + 86
3. Subtract 86n from both sides of the equation to isolate the variable:
87n - 86n + 82 = 86n - 86n + 86
n + 82 = 86
4. Finally, subtract 82 from both sides to solve for 'n':
n = 86 - 82
n = 4
Therefore, Risa took a total of (n + 1) tests including her Mathematics test.
(n + 1) = (4 + 1) = 5
Risa took 5 periodical tests, including her Mathematics test.