Solving a fraction word problem using a linear equation of the form Ax = B

Introduction

In this type of problems, we use linear equations of the form Ax = B.

B is given as a quantity which is a fractional part (A) of another unknown quantity x.

So, A and B are given and x is to be found here.

Rules to be followed while solving linear equations of the form Ax = B

The quantity A is usually a fraction and B is a whole number or decimal.
There is multiplying/dividing on both sides of the equation to isolate the unknown variable x.
Cross multiplying is done, if required, and the equation is solved to get the value of x.

Some solved examples given below will help in understanding the lesson.

Example 1:

A store sold 35 video game consoles on a single day which is one-ninth of their monthly sales. What is then the monthly sales of the store?

Step 1:

Let the number of game consoles sold in a month = x; Then given $35 = \frac{1x}{9}$

Step 2:

Cross multiplying

x = 35 × 9 = 315

So, total number of game consoles sold in a month = 315

Example 2:

Jeanie traveled 15 kilometers of her journey, which is one-eighth of total journey. How long is her total journey then?

Step 1:

Let the total journey in kilometers be = x; Then given $15 = \frac{1x}{8}$

Step 2:

Cross multiplying

x = 15 × 8 = 120

So, total journey in kilometers = 120 km