Question

Alice thinks of a number and subtracts
$\frac{3}{2}$ from it. She then multiplies the result by $8$. The result obtained is $5$ times the number she first thought of. What is the number Alice thought of?

• A. $4$
• B. $8$
• C. $10$
• D. $6$

Answer 1

The correct option is A $4$

Let the number that Alice initially thought of be $x$.
She subtracts $\frac{3}{2}$ from $x$ and then multiplies it by $8$.
The resultant number becomes: $\left(\right(x-\frac{3}{2})\times 8$

According to the question,
$(x-\frac{3}{2})8=5\times x$
$\Rightarrow (x\times 8)-(\frac{3}{2}\times 8)=5x$
$\Rightarrow 8x-12=5x$
$\Rightarrow 8x-5x=12$
$\Rightarrow 3x=12$
$\Rightarrow x=\frac{12}{3}$
$\Rightarrow x=4$

Thus, the number Alice initially thought of is $4.$