Question

Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. the result now obtained is three times the same number the thought of. what is the number?

Answer 1

Let the number Amina thinks of be \( x \).

According to the problem, she first subtracts \( \frac{5}{2} \) from \( x \):

\[
x - \frac{5}{2}
\]

Next, she multiplies the result by 8:

\[
8 \left( x - \frac{5}{2} \right)
\]

According to the problem, this result is equal to three times the number she thought of, which is \( 3x \). Therefore, we can set up the equation:

\[
8 \left( x - \frac{5}{2} \right) = 3x
\]

Now, we simplify the left side of the equation:

\[
8x - 8 \cdot \frac{5}{2} = 3x
\]
\[
8x - 20 = 3x
\]

Next, we can isolate \( x \) by moving \( 3x \) to the left side of the equation:

\[
8x - 3x - 20 = 0
\]
\[
5x - 20 = 0
\]

Adding 20 to both sides gives:

\[
5x = 20
\]

Now, divide both sides by 5:

\[
x = 4
\]

Thus, the number Amina thought of is \( \boxed{4} \).