Question

A number is 42 more than its half. The number is.

Answer 1

Hint: Now in the given problem we have given that the number is 42 more than its half. To solve this problem let us assume the number to be x. Now according to the problem we have that $x=42+\dfrac{x}{2}$ . This is an equation in one variable. Hence we can solve it to find the value of x.

Complete step-by-step answer:
Now we are given with a word problem which says a number is 42 more than it half. The number is.
Now let us try to understand the statement mathematically.
Now 42 more means nothing but $42+$ and half of the number means nothing but $\dfrac{1}{2}$ times the number.
Hence we have something like,
The number = 42 + $\dfrac{1}{2}$ times the number.
Now let us take the required number to be x.
Hence we have $x=42+\dfrac{1}{2}\times x..................(1)$
Now we know that $\dfrac{1}{2}\times x$ is equal to $\dfrac{x}{2}$
Hence using in equation (1) let us write $\dfrac{1}{2}\times x$ as $\dfrac{x}{2}$
$x=42+\dfrac{x}{2}$
Now multiplying the whole equation by 2 we get
$2\times x=42\times 2+2\times \dfrac{x}{2}............(2)$
Now we know that $\dfrac{x}{2}\times 2=x$ and 42 × 2 = 84, hence using this we get equation (2) as
$2x=84+x$
Now in the above equation subtracting x on both sides we get
$2x-x=84+x-x$
Now we know that x – x = 0, and 2x – x = x.
Hence we have
x = 84 + 0
x = 84
Now x is nothing but the required number.
Hence we have the required number is 84.

Note: Note that in word problems 42 more means addition of 42 and 2 times means multiplication of 2. Not to be confused between these terms.