Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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

?