A school has 200 students.

Question

Question

A school has 200 students. One third of the boys have blue eyes,and one quarter of the girls have blue eyes. Given that a total of 57 students have blue eyes,how many boys attend the school?

Answer 1

A table is quite useful for such problems.

 

              Blue eyes          Other color eyes       Total

Boys          B/3                           ?                    B

Girls           G/4                           ?                   G

Total           57                            ?                 200

 

B/3 + G/4 = 57       [eq1]         "1/3 of boys and 1/4 of girls ... total 57"

B   +  G = 200          [eq2]              "school has 200 students"

 

The math:

     4B + 3G =   684            [the LCM of 12; 12*eq1]

     3B + 3G =   600             [3*eq2]

  -----------------------      [elimination; subtract equations[

      B          =     84

Answer 2

Hi Binita,

We just need to build an equation based on the information we have, then solve it.

We know there are 200 students in the school.

Lets say x students are boys.

That means that the number of girl students is 200-x.

 

Now lets work out an equation for the number of students with blue eyes:

We know:

57 students have blue eyes

1/3 of boys have blue eyes

1/4 of girls have blue eyes

so...

(total number of boys)/3 = boys with blue eyes

(total number of girls)/4 = girls with blue eyes

(total number of boys)/3 + (total number of girls)/4 = total number of students with blue eyes = 57

 

We substitute the x values we defined in the first step into this equation:

total number of boys = x

total number of girls = 200-x

x/3+(200-x)/4 = 57

Then we simplify the equation and solve for x:

x/3+50-x/4 =57

x/3-x/4=7

x/3-x/4=7

Find a lowest common denominator for the fractions:

4x/12-3x/12 =7

x/12=7

x=84

So there are 84 boys in the school.

 

Hope this helps.  Message me if you have any questions.