Questions & Answers

The monthly salary S of a shop assistant is a sum of a fixed salary of \[\$500\] plus 5% of monthly sales. What should be her monthly sales so that the monthly salary reaches \[\$1500\]?

Answer Verified Verified
Hint: Here we will first let the monthly sales to be \[x\] and the form a linear equation with the help of given data and solve for \[x\] to get the desired value of monthly sales.
A linear equation in one variable is an equation in which the highest power of the variable is one and has one variable only.

Complete step by step solution:
Let the monthly sales be \[x\].
Since it is given that a monthly salary of $S$ is the sum of \[\$500\] plus $5\%$ of monthly sales.
Therefore, the monthly salary $S$ is given by:-
\[ {\text{S}} = 500 + 5\% {\text{ of x}} \]
$\Rightarrow {\text{S = 500}} + \dfrac{5}{{100}}x $
On simplification,
$\Rightarrow {\text{S = 500}} + \dfrac{x}{{20}}..............\left( 1 \right) $
Since it is given that the monthly salary should be \[\$1500\]
\[\Rightarrow S = \$ 1500\]
Substituting the value of S in equation (1) we get:-
\[\Rightarrow {\text{S = 500}} + \dfrac{x}{{20}} \]
$\Rightarrow 1500 = 500 + \dfrac{x}{{20}}$
On simplification of the above values,
$\Rightarrow 1500 - 500 = \dfrac{x}{{20}}$
$\Rightarrow \dfrac{x}{{20}} = 1000 $
On further simplification,
$\Rightarrow x = 1000 \times 20 $
$\Rightarrow x = 20,000 $

$\therefore$ The monthly sales should be $20000.

A student might make mistake in forming the linear equation.
So one should first understand the given information first and then make the equation using the following statement:-
Total salary = fixed salary + 5% of monthly sales.
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