1. 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?

Let the number be x.
Condition I: x – \(\frac { 5 }{ 2 }\)

Condition II: 8 × (x – \(\frac { 5 }{ 2 }\))

Condition III: 8 × (x – \(\frac { 5 }{ 2 }\)) = 3x

\(\Rightarrow\) 8x – \(\frac { 5 }{ 2 }\) × 8 = 3x [Solving the bracket]

\(\Rightarrow\)8x – 20 = 3x

\(\Rightarrow\) 8x – 3x = 20 [Transposing 3x to LHS and 20 to RHS]

\(\Rightarrow\) 5x = 20

\(\Rightarrow\) x = 20 ÷ 5 = 4 [Transposing 5 to RHS]

Hence, x = 4 is the required number.