Question 416040: There are 48 members of the band. Of these, 10 are left-handed and 19 wear eyeglasses. There are 27 members who are NOT left-handed and do NOT wear eyeglasses. How many left-handed members wear eyeglasses?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! There are 48 members of the band. Of these, 10 are left-handed and 19 wear eyeglasses. There are 27 members who are NOT left-handed and do NOT wear eyeglasses. How many left-handed members wear eyeglasses?
Make this chart:
Wear eyeglasses Dont wear eyeglasses Totals
Left-handed | | |
------------------------------------------------------------------
Right-handed | | |
------------------------------------------------------------------
Totals | | |
Fill in 48 for the total number of band members in the lower right corner.
Fill in 10 for the total number that are left-handed in the bottom cell in
the "wear eyeglasses" column.
Fill in 27 for the number of members who are NOT left-handed (right-handed)
and do NOT wear eyeglasses in the cell that is in the Right-handed
(NOT left-handed) row and in the "Don't-wear eyeglasses" column:
Wear eyeglasses Don't wear eyeglasses Totals
Left-handed | | | 10
------------------------------------------------------------------
Right-handed | | 27 |
------------------------------------------------------------------
Totals | 19 | | 48
Since everybody in the band either wears eyeglasses or don't, then
we can fill in the total that don't wear eyeglasses by subtracting
the number that do wear them which is 19, from the total number of
band members, 48, and get 29, so we fill that in the total that don't
wear eyeglasses:
Wear eyeglasses Don't wear eyeglasses Totals
Left-handed | | | 10
------------------------------------------------------------------
Right-handed | | 27 |
------------------------------------------------------------------
Totals | 19 | 29 | 48
Since everybody in the band is either left-handed or right-handed,
then we can fill in the total that are right-handed by subtracting
the number that are left handed, which is 10, from the total number of
band members, 48, and get 38, so we fill that in the total that are
right handed.
Wear eyeglasses Don't wear eyeglasses Totals
Left-handed | | | 10
------------------------------------------------------------------
Right-handed | | 27 | 38
------------------------------------------------------------------
Totals | 19 | 29 | 48
Since the total number who are right handed is 38, and 27 of these
right-handed members don't wear glases, the rest of the 38 right-handed
members do wear them, so we can fill in the number of right-handed members
who do wear glasses by subtracting 27 from 38, getting 11. So we can fill in
11 as the number of right-handed members who wear eyeglasses:
Wear eyeglasses Don't wear eyeglasses Totals
Left-handed | | | 10
------------------------------------------------------------------
Right-handed | 11 | 27 | 38
------------------------------------------------------------------
Totals | 19 | 29 | 48
Since the total number who don't wear eyeglasses is 29, and 27 of those
are right-handed, the rest of the 29 members who don't wear eyeglasses are
left-handed, so we can fill in the number of left-handed members who do
not wear glasses by subtracting 27 from 29, getting 2. So we can fill in
2 as the number of left-handed members who don't wear eyeglasses:
Wear eyeglasses Don't wear eyeglasses Totals
Left-handed | | 2 | 10
------------------------------------------------------------------
Right-handed | 11 | 27 | 38
------------------------------------------------------------------
Totals | 19 | 29 | 48
There are two ways to determine the number to put in the remaining cell.
Since the total number who wear eyeglasses is 19, and 11 of those
are right-handed, the rest of the 19 members who wear eyeglasses are
left-handed, so we can fill in the number of left-handed members who
wear glasses by subtracting 11 from 19, getting 8. We could
also have found this number 8 by subtracting the 2 lefties who don't
wear glasses from the 10 total lefties and gotten 8. So we can fill in
8 as the number of left-handed members who wear eyeglasses.
Wear eyeglasses Don't wear eyeglasses Totals
Left-handed | 8 | 2 | 10
------------------------------------------------------------------
Right-handed | 11 | 27 | 38
------------------------------------------------------------------
Totals | 19 | 29 | 48
So the answer is: 8 left-handed members wear eyeglasses.
Edwin
|
|
|
