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 ?

1

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4

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Solution

The correct option is C: $4$
Let the number Amina thought be $x$ .
First she subtract $\frac{5}{2}$ from the number
$∴$ $(x - \frac{5}{2})$ will be the result after subtraction.
Then, she multiplied 8, which means $(x - \frac{5}{2}) \times 8$ , is the result after multiplication.
According to the given question, we have
$the final result$ $= 3 \times the original no.$
$∴ 8 (x - \frac{5}{2}) = 3 x$
$\Rightarrow 8 x - 20 = 3 x$
$\Rightarrow 8 x - 3 x = 20$
$\Rightarrow 5 x = 20$
$\Rightarrow x = \frac{20}{5} = 4$
Hence, the number thought by Amina is $4$ .

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