Neema did y tests and scored a total of 120 marks. she did two more tests which she scored 13 and 14 marks. The mean score of the first y tests was 3 marks more than the mean score for all the tests she did. Find the total number of tests that she did.
Mean of first set of tests = 120/y
Mean after 2 more tests = 147/(y+2)
120/y - 147/(y+2) = 3
the LCD is y(y+2) , so multiplying each term by that ....
120(y+2) - 147y = 3y(y+2)
solve the quadratic using your favourite method, it comes out nicely.
If the mean of the y tests was x, then
y*x = 120
x = 3+(120+13+14)/(y+2) = 3(y+51)/(y+2)
so,
3y(y+51)/(y+2) = 120
y = 5
so, the mean of the 1st 5 tests was 24
total points was 120+13+14=147
The mean of all 7 tests = 147/7 = 21, 3 less than the first mean.
David has scored 81
, 88
, 93
, and 65
on his previous four tests. What score does he need on his next test so that his average (mean) is 80
?
To solve this problem, let's break it down step by step:
Let's assume that the total number of tests that Neema did is represented by "x."
We know that she did y tests and scored a total of 120 marks. Since the mean (average) score is calculated by dividing the total sum by the number of tests, we can write the equation:
(120 / y) = average score of the first y tests
We are also given that Neema did two more tests, and she scored 13 and 14 marks on those tests. So, the new total sum of all the tests will be (120 + 13 + 14).
Since the mean score of the first y tests was 3 marks more than the mean score for all the tests, we can write another equation:
(120 / y) - 3 = [(120 + 13 + 14) / (y + 2)],
Simplifying this equation will help us find the total number of tests (x) that Neema did.
Let's multiply both sides of the equation by (y + 2) to eliminate the denominator:
120(y + 2) - 3(y + 2) = (120 + 13 + 14)y,
120y + 240 - 3y - 6 = 147y + 47,
Simplifying further:
117y + 234 = 147y + 47,
Subtracting 117y and 47 from both sides:
234 - 47 = 147y - 117y,
187 = 30y,
Finally, dividing both sides of the equation by 30:
y = 187 / 30,
y ≈ 6.23.
Since y represents the number of tests Neema did, it must be a whole number. Therefore, we round up to the nearest whole number:
y = 7.
Thus, the total number of tests Neema did is x = y + 2 = 7 + 2 = 9.