Averages??

Question

A group of 5 students have an average age of 15. When another student joins the group the average changes to 14. How old was this student?

I have a feeling this type of question is pretty simple, but i just can't do it. If i could just see the process then that would be great. Thanks.

Answer 1

Yes this type of question can get trippy. The trick is you know how many students there are:

Suppose the first five students are named Alice, Bob, Carol, Dave, and Elise. And the new student, lets call him Frank.

Then you have the averages:

(A+B+C+D+E)/5=15
(A+B+C+D+E+F)/6=14

You can rewrite the first equation as:
(A+B+C+D+E)/5*5=15*5=75
so
(A+B+C+D+E)=75

Then you can substitute that into the second equation
(A+B+C+D+E+F)/6=(75+F)/6=14

Solving for F we get F=14*6-75=9

So Frank, the new guy, is 9 years old!

Answer 2

The total age of the 5 students is 5 x 15 =75

The total age of the 6 students is 6 x 14 = 84

Therefore the last student is 84 - 75 = 9yrs old

Answer 3

Yes this type of question can get tricky. The trick is to know how many students there are:

Suppose the first five students are named Alex, Beryl, Caarolinel, David, and Emma. And the new student, lets call him Fred

Then you have the averages:

(A+B+C+D+E)/5=15
(A+B+C+D+E+F)/6=14

You can rewrite the first equation as:
(A+B+C+D+E)/5*5=15*5=75
so
(A+B+C+D+E)=75

Then you can substitute that into the second equation
(A+B+C+D+E+F)/6=(75+F)/6=14

Solving for F we get F=14*6-75=9

So Frank, the new guy, is 9 years old!

Answer 4

Simple.
The 5 kids ages = 75 (5 x 15)
The 6 kids ages = 84 (6 x 14)

The sixths kids age is 9 (84 - 75)

Job done!

Answer 5

Let the first 5 students be a,b,c,d and e. So we have

(a+b+c+d+e)/5 = 15

Multiply both sides by 5 gives:

a+b+c+d+e = 75 ......Equation (1)

Now add the 6th student and you have:

(a+b+c+d+e+f)/6 = 14

Multiply both sides by 6 and you get:

a+b+c+d+e+f = 84 ..... Equation (2)

Take (1) from (2) and you get f = 9

So the age of the 6th student is 9 years.

Answer 6

9 5 x 15 years average age mean that the total age of the 5 students is 75

If the average age of 6 stdents in 14 then their total age is 6x14 = 84

84 - 75 = 9 the new student is therefore 9 years old.

Answer 7

sum of the ages of first 5 students is 5 *15=75
sum of 6 students is 14* 6=84

age of the 6th student is 84-75=09

9 years is the age added of the student

Answer 8

we know that average of 5 people a,b,c,d,e is a+b+c+d+e divided by the number of addends
(a+b+c+d+e)/5=15
transpose 5 it became *
(a+b+C+d+e)=5*15
a+b+c+d+e=75

after adding f the average become 14

(a+b+c+d+e+f)/6=14

we then substitute a+b+c+d+e as 75
(75+f)/6=14

transpose /6 become *6
75+f=14*6
75+f=84
transpose +75 to become -75
f=84-75
f=9
then the answer is 9

Answer 9

Total marks = 75
New total = 75 + x
New average = (75 + x) / 6
(75 + x) / 6 = 14
75 + x = 84
x = 9
Student was 9 years old.

Answer 10

average age of one student =15yrs. total age of 5 students =5 x15
=75yrs.
1 student increased average age became =14 yrs.
thus total age of 6 students =6 x14
=84 yrs.
age of 6th student is= (age of 6) - (age of 5)
=84 - 75
=9yrs.