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# 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.