Question

If \[x \times 15 = 37.5\% \] of \[220\]. Find \[x\]

Answer 1

Hint:
Here, we will write the percentage in fraction form. Then we will write the decimal number into fraction. We will then simplify the equation using basic mathematical operations like multiplication and division to get the required value.

Complete step by step solution:
We are given that \[x \times 15 = 37.5\% \] of \[220\].
Now, we will rewrite the percentage in the form of fractions, we get
\[ \Rightarrow 15x = \dfrac{{37.5}}{{100}} \times {\rm{220}}\]
Now, we will rewrite the decimal in the form of fractions, we get
\[ \Rightarrow 15x = \dfrac{{375}}{{1000}} \times {\rm{220}}\]
By simplifying the equation, we get
\[ \Rightarrow 15x = \dfrac{{375}}{{100}} \times {\rm{22}}\]
Dividing numerator and denominator by 5, we get
\[ \Rightarrow 15x = \dfrac{{75}}{{20}} \times {\rm{22}}\]
Now dividing 22 and 20 by 2, we get
\[ \Rightarrow 15x = \dfrac{{75}}{{10}} \times 11\]
Dividing both side by 15, we get
\[ \Rightarrow x = \dfrac{{75}}{{10 \times 15}} \times 11\]
Again dividing numerator and denominator by 15, we get
\[ \Rightarrow x = \dfrac{5}{{10}} \times 11\]
Multiplying the terms, we get

\[ \Rightarrow x = \dfrac{{11}}{2}\]
Therefore, the value of \[x\] is \[\dfrac{{11}}{2}\].

Note:
We are given a linear equation. Linear equation is an equation of a variable with the highest power as 1. Percentage is defined as the ratio or number expressed as a fraction of 100. We should know clearly that if the given values are in percentage, then the total of the value becomes 100 automatically, since the percentage represents a fraction by 100. While converting into a decimal we should also know that if a decimal number is multiplied by the powers of 10, then the decimal moves towards the right and if a decimal number is divided by the powers of 10, then the decimal moves towards the left. If the number of variables is less then it is easier to solve for the variable with the given conditions.