Question

Find a number if one-tenth of it when added to its one-ninth gives\[19\].

Answer 1

Hint: We will have to make an assumption about the number. The question is telling us that the sum of two fractions of the assumed number will give us another number. We will have to form a linear equation.

Complete step-by-step answer:
We will assume that let the required number be \[x\].
According to the given question, one-tenth of the number and one-ninth of the number give a sum of \[19\].
One tenth of the number\[ = \dfrac{1}{{10}}x\]
And one ninth of the number\[ = \dfrac{1}{9}x\]
So, we can write this as \[\dfrac{1}{{10}}x + \dfrac{1}{9}x = 19\].
Now, we will solve the equation to find the value of \[x\].
\[\dfrac{1}{{10}}x + \dfrac{1}{9}x = 19\]
We now take the LCM of the denominators,
\[
   \Rightarrow \dfrac{{9x + 10x}}{{90}} = 19 \\
   \Rightarrow \dfrac{{19x}}{{90}} = 19 \\
   \Rightarrow x = 19 \times \dfrac{{90}}{{19}} \\
   \Rightarrow x = 90 \\
\]
Therefore, the required number is \[90\].

Note: By reading the problem, we get to know that this is simple equation formation. We simply assume a number and proceed further as asked by the problem to form the required equation so that we can solve it further and find the assumed number.