Question

Find a number whose double is 45 greater than its half.

Answer 1

Hint:
Here, we will assume the number to be some variable. Then we will frame a linear equation from the given statement and solve the linear equation in one variable to find the number. A linear equation is defined as an equation having the highest degree of variable as 1.

Complete step by step solution:
Let \[x\] be the required number.
Now the double of a number will be \[2x\] and the half of a number will be \[\dfrac{x}{2}\].
Since we are given that a number whose double is 45 greater than its half, so mathematically we can write
\[2x = \dfrac{x}{2} + 45\]
By rewriting the equation, we get
\[ \Rightarrow 2x - \dfrac{x}{2} = 45\]
Taking LCM on LHS, we get
\[ \Rightarrow 2x \times \dfrac{2}{2} - \dfrac{x}{2} = 45\]
By simplifying the equation, we get
\[ \Rightarrow \dfrac{{4x}}{2} - \dfrac{x}{2} = 45\]
\[ \Rightarrow \dfrac{{4x - x}}{2} = 45\]
Subtracting the terms in the denominator, we get
\[ \Rightarrow \dfrac{{3x}}{2} = 45\]
Multiplying both sides by 2, we get
\[ \Rightarrow 3x = 45 \times 2\]

\[ \Rightarrow 3x = 90\]
Dividing both sides by 3, we get
\[ \Rightarrow x = \dfrac{{90}}{3}\]
\[ \Rightarrow x = 30\]

Therefore, the number whose double is 45 greater than its half is \[30\].

Note:
We know that Linear equations are a combination of constants and variables. Constants are the numbers whereas variables are represented in letters. Every linear equation in one variable has a one and unique solution. We have to put the variable on the left-hand side and the numerical values on the right-hand side and then Change the operators’ sign while changing sides of the terms thus we can solve for the variable. The graph of a linear equation is always a straight line whereas the graph of a quadratic equation is a curve.