If the ratios between boys and girls are 3:7 and there are 200 more girls than boys how many boys are there?

Question

 Can You Help Me with this question?

Answer 1

b represents the number of boys

b + 200 represents the number of girls

 

3:7 :: b:b+200           product of means and extremes

3(b + 200) = 7b         distribute

3b + 600 = 7b            subtract 3b from both sides

600 = 4b                   divide both sides by 4

150 = b

 

There are 150 boys.

Answer 2

None!

 

Boys are scared of that many Girl Cooties and ran away like bats out of Hell!

Answer 3

Two numbers x and y have the ratio a:b if there is an number n such that a*n=x and b*n=y.

 

Let x=number of boys

     y=number of girls

 

The problem gives the ratio 3:7.  That means for each group of 3 boys there is a group of 7 girls.  The possibilities are:

    n       x=a*n  (boys)              y=b*n (girls)

    1          3                                   7

    2          6                                 14

    3          9                                 21

 ...

 

Notice the number of girls more than the number of boys in this list.  We need to find x and y where the difference is 200.

We'll do that by finding the value of n.

 

 y  -  x  = 200            [200 more girls than boys)

7n - 3n = 200            [7 girls for 3 boys]

     4n  =  200

      n = 50               [there are 50 groups of 3 and 7]

x = 3n = 150 boys

Answer 4

Let B = # boys, G = # girls

 

1) B/G = 3/7

 

2) G = B + 200

 

Substitute G into eq. 1: B/(B + 200) = 3/7

 

Rearrange that to get 7/3 = 1 + 200/B

 

Rearrange that to get 4/3 = 200/B

 

Solve for B = 150

Solve for G by plugging back into eq. 2: G = 350.

Answer 5

b= boys

g= girls

 

b/g = 3/7 ----->7b=3g

 

g=200+b (girls are 200 more than boys)

 

7b=3(200+b)

7b=600+3b ----->4b=600 ---->b=150

 

There are 150 boys