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

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.

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?

Solution

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

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

Solution

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