Star Problem: Ratio of girls and boys in a class

Star Problem: Ratio of girls and boys in a class

Problem:

There are 40 pupils in a class. Each girl is given 5 books and each boy is given 3 books. The girls have 128 more books than the boys. How many girls are there in the class?

Given:

40 pupils

5 books each girl = 5 books / girl

3 books each boy = 3 books / boy

Girls have 128 more books than the boys

Asked:

How many girls are there in the class?

Solution:

LET:  Gnumber of girls in the classBnumber of boys in the class

Total books of the girls  =   number of books each girl  x   number of girls in the class   NS*. 1

Total books of the girls  =  ( 5 books / girl )  x  G

Total books of the girls  =  5G  Eq. 1

Total books of the boys  =  number of books each boy  x  number of boys in the class     NS. 2

Total books of the boys  =  ( 3 books / boy )   x  B

Total books of the boys  =  3B   Eq. 2

It was given that, the Girls have 128 more books than the boys; using comparing entities, we have the following *Number Sentence (NS) :

Total books of the girls  =  Total books of the boys  +  128   NS. 3

Substituting, Equations (Eq.) 1 & 2 on NS. 3, we have:

5G   =   3B   +  128    Eq. 3

The problem hinted us that there were 40 pupils; the pupils consists of girls and boys, hence, we have the following Number Sentence (NS):

Number of girls in the class  +  Number of boys in the class  =  40

G  +  B  =  40    Eq. 4

Manipulating Eq. 4, we get:

B  =  40  –  G    Eq. 4a

Substituting Eq. 4a on Eq. 3, we get:

5G  =  3(40  –  G)  +  128

Simplifying:

5G  =  120  –  3G  +  128

5G  +  3G  =  120  +  128

8G  =  248

8G / 8  =  248 / 8

G  =  31   Ans. There are 31 girls in the class

Using Eq. 4a, we get the number of boys in the class

B  =  40  –  G

B  =  40  –  31

B  =  9  Ans. There are 9 boys in the class

Checking:

Using Eq. 1,  Total books of the girls = 5G, we get :

5G = (5 books/girl)  x  31 girls = 155 books

Using Eq. 2, Total books of the boys = 3G, we get :

3G = (3 books/boy) x  9  boys = 27 books

Using NS. 3,

Total books of the girls  =  Total books of the boys  +  128

Total books of the girls  =  27 books  +  128

Total books of the girls  =  155 books

2 Replies to “Star Problem: Ratio of girls and boys in a class”

  1. My heartfelt thanks for the quick reply! My daughter is happy she has completed her homework before going to school. Homeworkz now will be our bestfriend in the coming days!

  2. hi missy,

    you’re welcome 🙂 sorry for the late reply, i’ve been busy lately. but anyhow, please feel free to post your questions & i’ll try my best to reply as soon as i can.

    thanks

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