question_answer 19)

                Amina thinks of a number and subtracts \[\frac{5}{2}\] from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?

Answer:

                Let the number be \[x\]. Then, according to the question,                 \[\left( x-\frac{5}{2} \right)\,8=3x\] \[\Rightarrow \]               \[8x-\frac{5}{2}\times 8=3x\] \[\Rightarrow \]               \[8x-20=3x\] \[\Rightarrow \]               \[8x-3x=20\]                      |Transposing \[3x\] to LHS and ? 20 to RHS \[\Rightarrow \]               \[5x=20\] \[\Rightarrow \]               \[x=\frac{20}{5}=4\]                       | Dividing both sides by 5 Hence, the required number is 4. Check: \[\left( 4-\frac{5}{2} \right)8=\frac{8-5}{2}\times 8\]                 \[=\frac{3}{2}\times 8=3\times 4=12\] \[3x=3\times 4=12\] Hence, the result is verified.