Problem solving questions PLEASE HELP ASAP

Question

I have a test tomorrow and not sure how to solve this question, can you please help.

12 people were walking home carrying a basket of fruit in each hand. If one half of the group did not have 2 baskets when they arrived home, and half of this number only had 1 basket, how many baskets of fruit were remaining when the group arrived home?

Answer 1

Assuming that the 12 people walking home constituted the group, then you have a total of 12 people to start off with each having 2 baskets (1 in each hand). When they got home, half of the group (6 people) did not have 2 baskets. So that means half of the group (6 people) did have 2 baskets. Our group now looks like this:

6 people have 2 baskets

6 people do not have 2 baskets

Assuming that these people did not gain baskets on their way home, that means that the 6 people who did not have 2 baskets had either 1 or 0 baskets when they got home. So we can rewrite the above as:

6 people have 2 baskets

6 people have 1 or 0 baskets

Half of the group that does not have 2 baskets only had 1 basket. So the half that does not have 2 baskets consists of 6 people. Half of this group of 6 is 3 people. Given that the option was either 1 or 0 baskets, that means that the other 3 people had 0 baskets. So now we can write the group as:

6 people have 2 baskets

3 people have 1 basket

3 people have 0 baskets

Let's figure out how many baskets there are in each subgroup:

6 people have 2 baskets so 6*2 = 12 baskets total in this subgroup

3 people have 1 basket so 3*1 = 3 baskets total in this subgroup

3 people have 0 baskets so 3*0 = 0 baskets total in this subgroup

Now to sum it all up, 12+3+0 = 15 total baskets remaining when the group arrived home.

Answer 2

“12 people were walking home carrying a basket of fruit in each hand”   That makes, at most, 24 baskets.

But, something happened to some baskets on the way home. Our answer should be less than 24.

“one half of the group did not have 2 baskets when they arrived home.” So, 6 people either had no baskets or they had one basket (they did not have 2 baskets).

“half of this number only had 1 basket.” This means that 3 people had 1 basket and 3 people had no baskets.



That makes –

      6 people with 2 baskets   --     12 baskets

      3 people with 1 basket    --        3 baskets

      3 people with no basket  --         0 baskets

                                            TOTAL: 15 baskets