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:  G – number of girls in the class;  B – number 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