Question

If 10 less than a number is 65, then find the number.

Answer 1

Hint:
Here, we need to find the number which when reduced by 10, gives 65 as the result. We will assume the number to be \[x\]. We will apply the given operations and obtain an equation in terms of \[x\]. We will then solve the equation to find the value of \[x\] and hence, find the required number.

Complete step by step solution:
Let the number be \[x\].
We need to apply the given operations on the number \[x\] and equate the result to 65 to obtain an equation in terms of \[x\].
First, we will subtract 10 from the number.
Subtracting 10 from \[x\], we get the expression
\[x - 10\]
Now, it is given that 10 less than the number is 65.
This means that the 10 less than \[x\] should be equal to 65.
Thus, we get the equation
\[x - 10 = 65\]
We need to solve this equation to get the value of \[x\] and hence, find the number.
Adding 10 to both sides of the equation, we get
\[ \Rightarrow x - 10 + 10 = 65 + 10\]
\[ \Rightarrow x = 75\]
Thus, we get the value of \[x\] as 75.

\[\therefore\] we get the number as 75.

Note:
We have formed a linear equation in one variable from the given information in this question. A linear equation in one variable is an equation of the form \[ax + b = 0\], where \[a\] and \[b\] are integers. A linear equation of the form \[ax + b = 0\] has only one solution.
We can verify our answer by applying the stated operations on the number 75.
Subtracting 10 from 75, we get \[75 - 10 = 65\].
Thus, if 10 less than a number is 65, then the number is 75.
Hence, we have verified our answer.