Question

$5$ times the difference of $29$ and a number is $215$ . How do you write this as an equation?

Answer 1

Hint: Conversion of words to equation only requires prioritisation of parts, so that defining the higher priority parts readily defines the lower priority ones. Here, the first priority goes to “a number”, so we assume it as $x$ which is the variable of the equation. Then, without defining ”the difference”, we cannot define its “5 times”, so “the difference” is of second priority and we write it as $29-x$ . Similarly, we find its $5$ times as $5\times \left( 29-x \right)$ and finally equate it to $215$ .

Complete step by step answer:
The required equation in words is given as
$5$ times the difference of $29$ and a number is $215$
First of all, we need to find what is the variable or unknown over here. Clearly, nothing is mentioned about “a number”. So, we consider it as $x$ , the variable of the equation.
Next, we see that “ $5$ times the difference of $29$ and a number” is mentioned. So, we first need to define what is “the difference”. Only then we can understand what the “ $5$ times of the difference” is.
Difference of $29$ and a number can be expressed as $29-x$ , as we already have assumed the unknown number to be $x$ .
“ $5$ times the difference” can now be expressed as $5\times \left( 29-x \right)$ . Finally, we can see that it is given that this “ $5$ times” is equal to $215$ . Therefore, we develop the equation as
$5\times \left( 29-x \right)=215$

Therefore, we can conclude that “ $5$ times the difference of $29$ and a number is $215$ ” can be written in equation as $5\times \left( 29-x \right)=215$

Note: During conversion of word format into an equation we must be careful about which part to develop first. Thus, we need to prioritise the parts of the sentence. We have to see which part if not defined, we cannot carry on the rest of the conversion and prioritise accordingly.