Given:
In a number, adding [tex]1\dfrac{3}{4}[/tex], then multiplying the result by [tex]2\dfrac{2}{11}[/tex] we get 8.
To find:
The unknown number.
Solution:
Let the unknown number be x.
According to the question,
[tex](x+1\dfrac{3}{4})\times 2\dfrac{2}{11}=8[/tex]
[tex](x+\dfrac{1\times 4+3}{4})\times \dfrac{2\times 11+2}{11}=8[/tex]
[tex](x+\dfrac{4+3}{4})\times \dfrac{22+2}{11}=8[/tex]
[tex](x+\dfrac{7}{4})\times \dfrac{24}{11}=8[/tex]
Multiply both sides by [tex]\dfrac{11}{24}[/tex].
[tex]x+\dfrac{7}{4}=8\times \dfrac{11}{24}[/tex]
[tex]x+\dfrac{7}{4}=\dfrac{11}{3}[/tex]
Subtract [tex]\dfrac{7}{4}[/tex] from both sides.
[tex]x=\dfrac{11}{3}-\dfrac{7}{4}[/tex]
[tex]x=\dfrac{44-21}{12}[/tex]
[tex]x=\dfrac{23}{12}[/tex]
[tex]x=1\dfrac{11}{12}[/tex]
Therefore, the required number is [tex]1\dfrac{11}{12}[/tex].
