Question

Express 107 in the form of \[4q + 3\] for some positive integer.

Answer 1

Hint:
Here we need to express the given number in the form of the given expression. For that, we will equate the given number with the given expression. From there, we will get the equation including the variable. Then we will simplify the equation to get the value of the variable and hence we will write the number in the form of the given expression.

Complete Step by Step Solution:
First, we will equate the given number i.e. 107 with the given expression i.e. \[4q + 3\].
On equating both of them, we get
\[4q + 3 = 107\]
Now, we will subtract 3 from both sides of the equation. Therefore, we get
\[ \Rightarrow 4q + 3 - 3 = 107 - 3\]
On further simplification, we get
\[ \Rightarrow 4q = 104\]
Now, we will divide both sides by the number 4. So, we get
\[ \Rightarrow \dfrac{{4q}}{4} = \dfrac{{104}}{4}\]
\[ \Rightarrow q = 26\]
Now, we will substitute the obtained value of \[q\] in the given expression \[4q + 3\]. Therefore, we get
\[ \Rightarrow 4q + 3 = 4 \times 26 + 3\]

Therefore, 107 can be written as \[4 \times 26 + 3\]

Note:
We need to remember that when we divide the given number 107 by 4, we will get the remainder as 3 and the divisor as 26. This expression also represents the remainder theorem which states that the dividend is equal to the sum of product of divisor and quotient and the remainder.
\[107 = 4 \times 26 + 3\]
Here 107 is the dividend, 26 is the quotient, 4 is the divisor and 3 is the remainder.
Here, we get the value of the one variable by solving one equation. In order to find the value of the given number of variables, we need the same number of equations to get the value of all the variables.