another math ratio problem

[Electrons]

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The ratio of boys to girls in a class was 2:3. Later when 15 boys joined the class, the ratio reversed. How many girls were in the class?

Answer: 18. How is this setup?

You know what's wierd is even if I plug in the answer it don't match up. I think this problem has a mistake somewhere.
Before:
B 36
G 54
ratio B:G matches 2:3

After:
B: 36 + 15 = 51
G: 54
ratio B:G (51:54) does not matches 3:2

 

[Danny289]

The ratio of boys to girls in a class was 2:3. Later when 15 boys joined the class, the ratio reversed. How many girls were in the class?

Answer: 18. How is this setup?

just right down the info:
b=boy g=girl

(b/g)=(2/3)
[(b+15)/g]= (3/2)
from equation 1 and 2 find b and g
that orginal boys 12 and girls 18 and you can see 12/18 is equal to 2/3 and after addind 15 boys we will have 27/18 is equal to 3/2
lol wait for streetwolf maybe he can explain in easier way

 

[PooyaH]

The ratio of boys to girls in a class was 2:3. Later when 15 boys joined the class, the ratio reversed. How many girls were in the class?

Answer: 18. How is this setup?

You know what's wierd is even if I plug in the answer it don't match up. I think this problem has a mistake somewhere.
Before:
B 36
G 54
ratio B:G matches 2:3

After:
B: 36 + 15 = 51
G: 54
ratio B:G (51:54) does not matches 3:2

I did it the same way as Danny!

b/g = 2/3.............so b = 2g/3
(b+15)/g = 3/2
2b + 30 = 3g
3g - 2b = 30
3g - 2(2g/3) = 30
3g - 4g/3 = 30
5g/3 = 30
5g = 90
g = 18

I hope there's a faster way to get there, right now my brain is not working! lol

 

[Electrons]

Thanks guys. I get it now. It would be nice if there's some quicker shortcut way.

 

[Streetwolf]

The ratio of boys to girls in a class was 2:3. Later when 15 boys joined the class, the ratio reversed. How many girls were in the class?

Answer: 18. How is this setup?

You know what's wierd is even if I plug in the answer it don't match up. I think this problem has a mistake somewhere.
Before:
B 36
G 54
ratio B:G matches 2:3

After:
B: 36 + 15 = 51
G: 54
ratio B:G (51:54) does not matches 3:2

Yeah the easier way is to keep the girl 'equivalent' the same. I think that word is my own creation but who knows. What I mean is that the original boy 'equivalent' is 2 and the original girl 'equivalent' is 3. There aren't 2 boys and 3 girls but imagine there were 12 boys. Then we're working with blocks of 6 here. You do 2*6 to get the boys and 3*6 to get the girls.

Since we are only changing the boys, you want to keep the girls the same. If the original ratio is 2:3 and the new ratio is 3:2, you want to look at the first ratio's 3 and the second ratio's 2. You can make them the same with a 6. So the first ratio will be 4:6 and the second will be 9:6. Since the number of girls HAVE NOT CHANGED and you have a 6 down for BOTH sets of girls, you must be multiplying the ratios by the SAME number. If the boys increased by 5 equivalents and the number of actual boys increased by 15, you want to multiply everything by 15/5 = 3. So the new number of boys is 9*3 = 27 and the new number of girls is 6*3 = 18.

 

[Electrons]

If the boys increased by 5 equivalents and the number of actual boys increased by 15, you want to multiply everything by 15/5 = 3. So the new number of boys is 9*3 = 27 and the new number of girls is 6*3 = 18.

"5 equivalents" where is that coming from? Is that from 2 in the initial ratio for the boys and 3 from the later ratio for boys?

 

[Streetwolf]

"5 equivalents" where is that coming from? Is that from 2 in the initial ratio for the boys and 3 from the later ratio for boys?

The new ratios are 9:6 and 4:6 with the original being 4:6. Remember that with ratios you multiply BOTH sides of the colon by the SAME number. When I write 'equivalents' that's just how I describe it. It's probably my own creation. If there were 40 boys in the 4:6 ratio, each 'equivalent' would contain 10 boys. When you look at the new ratio, the number of girls in the ratio is the SAME. Since the girls have not changed, you must be multiplying the numbers in the ratio by the same value. That means the BOYS are multiplied by the same number in BOTH ratios. In the first, the number of 'equivalents' is 4. In the second, when more boys are added, it is 9. That means 5 'equivalents' of boys have been added. Each 'equivalent' has the same amount of boys. If 15 boys were added in total, that means each 'equivalent' has 3 boys. So your magic number here would be 3.

That means you multiply the numbers in the ratio by 3 to get the actual numbers.


===

I came up with the word 'equivalent' because the sets are equal to each other. Each number in the ratio represents a group with a given number of objects in the set. But the number of objects in this set is the same for EVERY set. With the ratio of 3:2 for example, EACH set has the same number in the set. So if there were 3 girls for every 2 boys, you can imagine it as 3 groups of girls and 2 groups of guys. These groups have EQUAL numbers of people in them. If there are 20 people total, each group would have 4 people in it.