A Complicated Math Question! PLZ HELP??

Question

Johnny was ill and had to take a test a day late.
His 96 raised the class average from 71 to 72.

How many students INCLUDING Johnny took the test?

Show all work and explain!

Please help i cant figure it out....

Answer 1

Let s be the sum of the scores without Johnny's score and n be the number of kids in the class except Johnny.
s/n = 71 [this is the average score before Johnny takes it]
(s + 96) / (n + 1) = 72 [average after Johnny takes it]

s / n = 71
s = 71n

Substitute s = 71n into second equation:
(71n + 96) / (n + 1) = 72
Multiply both sides by n+1:
71n + 96 = 72(n + 1)
Distribute:
71n + 96 = 72n + 72
Combine like terms:
n = 24

Add Johnny:
n + 1 = 25

Answer 2

Let the number of students = n. Let the total score before John took the test = S.

Before John took the test, we have
S/(n-1) = 71,
i.e., S = 71n - 71.

After John took the test, we have
(S+96)/n = 72,
i.e., S + 96 = 72n.

Simultaneous equations! Subtract the first equation from the second to eliminate S:
96 = n + 71,
so n = 96 - 71.
That means that 25 students took the test.

Answer 3

The average is the total of all the scores, divided by the number of students.

Let's say there are x students besides Johnny, they all had a combined score of y. Then y / x = 71.

Johnny got a 96, which made the average 72, so this means
(96+y) / (x+1) = 72

You've got two equations with two unknowns. Find x+1, which is the number of students including Johnny.

Answer 4

Let n be the # that took the test without Johnny
the total score is 71n
Johnny took the test later and got 96
the new average = (71n + 96)/(n+1) = 72
71n + 96 = 72(n+1) = 72n + 72
n = 96 - 72 = 24

Including Johnny, n+1 = 25 took the test.

Answer 5

Let's use "n" as the number of people in the class, INCLUDING Johnny.

So, you are given that 96 + 71*(n-1) = 72*n
(Johnny's 96 + 71 for everybody else gives a class average of 72)

Now you can solve:
96 + 71n -71 = 72n
96-71 = n
n = 25

So there are 25 people in the class including Johnny.

Answer 6

the old class average was the total of their scores divided by the number of them, T/n = 71. including Johnny's score gives us (T+96)/(n+1) = 72. Solve the 1st one for T, T = 71n, and plug it into the 2nd:

(71n + 96)/(n+1) = 72
71n + 96 = 72(n+1)
71n + 96 = 72n + 72
24 = n,
so including Johnny, class size is 25.

Answer 7

let x = total number of student
[ 71 (x-1) + 96 ] / x = 72
71 x - 71 + 96 = 72 x
x = 25

Answer 8

96-71 = 25 students
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Ideas of mental math approach: 96-71 = 25 is the points above the average. Distributing 25 points to everyone, including Johnny to raise the average by 1 means there are 25 students.
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The guy above me put the answer later.

Answer 9

What grade are you in? Like 6th? That was REAL hard to me in 6th grade. It's still REAL hard to me now, but I'm getting where I know it. But I stink and HATE math!!! LOL.OK. Let's see. 71-72. 96,. I think the answers 25! But you might want to get the answer from someone else, because I SUCK at math!!!! LOL. I hope I helped!!! :)

Answer 10

Oh geez...
Ehh I hate Albegra.
I start Algebra II when I go back to school Thursday.
*Runs in fear.*
Geometry is soooo easy, Algebra I just suck at.