math question?

Question

the ratio of the number of boys to the number of girls in a group of students is 2:3. if 1/4 of the boys and 1/3 of the girls wear glasses, find the ratio of the number of girls who wear glasses to the number of boys who wear glasses. please tell me the answer & how you got it. Thanks.

Answer 1

2:1

3(1/3):2(1/4)
1:1/2 which is the same as 2:1

to verify, say there are 100 kids in the class.
40 kids would be boys and 60 girls
10 boys would wear glasses and 20 girls would wear glasses. that is a 2 to 1 ratio. Note: the question starts out with boys to girls ratio, but the answer is requested to be girls to boys ratio so that is why I flipped it around.

Answer 2

Don't let this kind of problem overwhelm you. Trust me, those of us who can do this kind of stuff don't see the answer immediately. Start by putting down what we do know; in this case:

boys/girls = B/G = 2/3 (no problem there, it's given)

Bg (boys who wear glasses) = B/4.
Gg = G/3 (also given)

Now you have to go to work. We're looking for the ratio of girls-glasses to boys-glasses. Write it down:

Gg/Bg would be, using what we already figured out:

Gg/Bg = (G/3) / (B/4)

ok, so now pause and think: what do we need to do to get rid of the lettered variables and reduce this thing to a ratio? At this point we don't know, but let's go back and look at the first equation:

B/G = 2/3, Great. that means B = 2G/3. If we substitute that into the above equation we can get rid of the B:

Gg/Bg = (G/3) / (B/4) = G/3 / (2G/3)/4

a bit messy, but reducible. First divide the num. and denom. by G to get rid of the G's, yielding:

Gg/Bg = 1/3 / (2/3)/4 Now get rid of the 4 by multiplying by 4/4 yielding:

Gg/Bg = (4/3) /( 2/3) Now you can multiply Num and Denom by 3, but look at it and you can see that four thirds over two thirds is just 2:1,

Gg/Bg = (4/3) /(2/3) = 4/2 =2.

Twice as many girls in this group wear glasses as boys. Cool. Word problems can be fun!

Answer 3

B denotes boys total
G denotes girls total
w denote wear glasses
B...4 units
G...6 units
Within B, there is 1 one unit of w.
Within G there is 2 unit of w/.
Therefore the ratio is 2:1

Answer 4

Maybe this help, but I am not sure.
I/4 of 2 is 0.50
1/3 of 3 is 0.75
So, 0.50 of boys and 0.75 of girls wear glasses.
So, 50% of boys and 75% of girls.
0.5:0.75

Answer 5

First of all you need to substitute the first ratio with some nunmbers so you can work it out, so we'll use 2:3=20:30. Next, you work the fractions into the ratio. (20*1/4=5)and(30*1/3=10).Now you take the answers and put them into a ratio and then simplify the ratio. 5:10=1:2. Now you know that 1:2 is your answer and it will come out true if you used a different number in the first step (boys:girls).

Answer 6

imagine theres 100students and use that

.

Answer 7

2x:3y where x is boys and y is girls.
1/4(2x) is the number of boys with glasses.
1/3 (3y) is the number of girls with glasses.
1/4(2x) is .5x
1/3 (3y) is 1y
.5:1 is the ratio, although it's a good idea to put it in integers:
1:2.

Answer 8

my exact work:
B:G
1/4x2 : 3x1/3
1/4x 2/1 2/4 1/2 B
3/1x 1/3 1G
ratio G:B 1/2:1

Answer 9

substitute easily usable numbers to solve this. Assume 100 students for ease. Then there would be 40 boys and 60 girls. So if 1/4 of the boys wear glasses--that would be 10. If 1/3 of the girls wear glasses, that would be 20. So...girls that wear glasses to boys is 20:10--simplified as TWO TO ONE.

Answer 10

Pick a number, since you're only interested in ratios, just choose something convenient. Let's say 50 students.

20 of them are boys
30 of them are girls

1/4 of the boys is 1/4 of 20, or 5
1/3 of the girls is 1/3 of 30, or 10

ratio of girls who wear glasses to boys who wear glasses is then
10:5 or 2:1