## 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**

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!

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