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?

Given:

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. 

To do:

We have to find the number.

Solution:

Let the number thought by Amina be $x$.

Amina thinks of a number and subtracts \( \frac{5}{2} \) from it.

This implies it is now equal to $x-\frac{5}{2}$.

Multiplying it by $8$, we get,

$8(x-\frac{5}{2})=8x-4\times5$

$=8x-20$

The result obtained is 3 times the same number she thought of.

Therefore,

$8x-20=3\times x$

$8x-20=3x$ 

$8x-3x=20$

$5x=20$

$x=\frac{20}{5}$

$x=4$

The required number is $4$. 

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Updated on: 10-Oct-2022

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