please answer this average question for me :)

Question

There are seven girls and three boys in a youth group. Then mean pocket money the girls recieve is £5.40. The mean pocket money the boys recieve is £4.80. Find the mean pocket money for the whole group.

Answer 1

Lets first represent the mean(average) of the girls:

 

(x₁+x₂+x₃+x₄+x₅+x₆+x₇)/7 = 5.40

 

Now we represent the boys:

 

(y₁+y₂+y₃)/3 = 4.80

 

To find the mean of the whole group you want to add x₁+...+x₇ + y₁+y₂+y₃ ( I did not want to rewrite all 7 money for the girls), and divide by how many people are in the whole group

Answer 2

you need to get the amount frome ach group individually before you can do the whole group.

 

girls get 5.40 per girl and there are 7 girls...5.40 x 7 = 37.80

 

boys get 4.80 per boy and there are 3 boys...4.80 x 3 = 14.40

 

so the total amount is 37.80+14.40 = 52.20

 

since we want this to be averaged over the whole group, we average it over 10 (7 girls +3boys)

 

52.20/10 = 5.22 per person.