- Equations and Applications
- Home
- Additive property of equality with decimals
- Multiplicative property of equality with decimals
- Multiplicative property of equality with whole numbers: Fractional answers
- Multiplicative property of equality with fractions
- Using two steps to solve an equation with whole numbers
- Solving an equation with parentheses
- Solving a fraction word problem using a linear equation of the form Ax = B
- Translating a sentence into a multi-step equation

# 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