HELp plsssssssssssss !?

Question

300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

Answer 1

x is students
y is apples

xy = 300 represents your first sentence
(x+10)(y-1) = 300 represents your second sentence
Solve the first equation for y...y=300/x...and sub into the second.

(x+10)(300/x - 1) = 300 Multiply this out and set = 0
x^2 + 10x - 3000 = 0 then factor
(x+60)(x-50) = 0
so x = 50
which means 50 students get 6 apples and 60 students get 5; but the ANSWER IS 50.


Note: seinchin's last step should be -60 and 50

Answer 2

If x is the original number of students and a is original the number of apples each student recieved:

ax = 300
(a -1)(x+10) = 300
substitute:
ax = (a -1)(x+10)
expand:
ax = ax +10a - x -10
isolate a:
a = (x+10)/10
substitute this into the original equation:
x(x+10)/10 = 300
solving for x:
x^2 + 10x = 3000
x^2 + 10x + 25 = 3000 + 25
(x+5)^2 = 3025
x + 5 = +/- 55
x = 60 or x = -50

x must be positive, so there were 60 students.

Answer 3

Because we are dealing with people and assuming the apples are not chopped into parts, then all the numbers will be full numbers (natural numbers).
If there was one student to start off with, he/she would get all 300 apples.
If there were two students to start off with they would get 150 apples each.
Make a list.
S - Student.
A - No. of Apples.

1s - 300a.
2s - 150a.
3s - 100a.
4s - 75a.
5s - 60a.
6s - 50a.
10s - 30a.
12s - 25a.
15s - 20a.
20s - 15a.
25s - 12a.
30s - 10a.
50s - 6a.
60s - 5a.
75s - 4a.
100s - 3a.
150s - 2a.
300s - 1a.

Now search the numbers to identify a solution to the answer.
It can be seen from the list, having 50 and 60 students satisfy the answer.

Answer 4

50 students each got 6 apples. with 60, they would have gotten 5 apples each