To solve the problem step-by-step, let's follow the instructions given in the problem.
1. Define the unknown number:
Let [tex]\( x \)[/tex] be the number that Amina thinks of.
2. Subtract [tex]\( \frac{5}{2} \)[/tex] from [tex]\( x \)[/tex]:
The expression for this step is:
[tex]\[
x - \frac{5}{2}
\][/tex]
3. Multiply the result by 8:
The expression now becomes:
[tex]\[
8 \left( x - \frac{5}{2} \right)
\][/tex]
4. Set this equal to 3 times the original number:
According to the problem, the result obtained after multiplying by 8 is equal to 3 times the number [tex]\( x \)[/tex]. So, we set up the equation:
[tex]\[
8 \left( x - \frac{5}{2} \right) = 3x
\][/tex]
5. Simplify the equation:
First, distribute the 8 inside the parentheses:
[tex]\[
8x - 8 \cdot \frac{5}{2} = 3x
\][/tex]
Simplify the multiplication:
[tex]\[
8x - 20 = 3x
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], subtract [tex]\( 3x \)[/tex] from both sides of the equation:
[tex]\[
8x - 3x - 20 = 0
\][/tex]
Simplify:
[tex]\[
5x - 20 = 0
\][/tex]
Add 20 to both sides:
[tex]\[
5x = 20
\][/tex]
Divide both sides by 5:
[tex]\[
x = 4
\][/tex]
So, the number Amina thinks of is:
[tex]\[
x = 4
\][/tex]
Therefore, the number Amina thinks of is [tex]\( 4 \)[/tex].
