Question

How do you find a number which exceeds $10$ by as much as twice the number exceeds $38$?

Answer 1

Hint: In this question we will first convert the word problem in the mathematical form such that it becomes an equation. We will then rearrange the terms in the expression and get the value of the required number. We will consider the unknown number to be $x$ and make the expression accordingly.

Complete step by step solution:
We have to find a number which exceeds $10$ by as much as twice the number exceeds $38$.
Consider the unknown number to be $x$, we know that the number exceeds $10$ which means that whatever be the value of $x$, it has been exceeded by $10$ therefore, to get the value of the number, we will have to subtract the value by $10$.
Therefore, the left-hand side of the expression will be $x-10$.
Now we know that twice the number exceeds 38 which means that when the number is multiplied twice which means $2x$, it is exceeded by $38$ which means we have to subtract $38$ from $2x$.
Therefore, the right-hand side of the expression will be $2x-38$.
On writing both the sides and equating, we get:
$x-10=2x-38$
On taking like terms together, we get:
$38-10=2x-x$
On simplifying, we get:
$28=x$, which is the required number.

Note:
Now to verify whether the solution is correct, we will cross check the values. The number which exceeds $10$ by as much as twice the number exceeds $38$.
We can see that:
$2\times 28-38=18$ and $28-10=18$ therefore, the solution is correct.
It is to be remembered that the equation given above is a linear equation which has only one variable which is $x$.