Let's break down the problem step-by-step.
1. Understanding the problem: We know that after a 25% reduction, an additional [tex]$4.00 was deducted, leaving the final price of the table at $[/tex]84.50. We need to write an equation to find the original price, [tex]\( x \)[/tex].
2. Account for the 25% reduction:
- A 25% reduction means 75% of the original price remained.
- Mathematically, if [tex]\( x \)[/tex] represents the original price, 75% of [tex]\( x \)[/tex] is [tex]\( 0.75x \)[/tex].
3. Deducting an additional [tex]$4.00:
- After the 25% reduction, we deduct another $[/tex]4.00 from the price.
- The price after the additional deduction is [tex]\( 0.75x - 4.00 \)[/tex].
4. Set the final price:
- After both reductions, the final price of the table is set to be $84.50.
- Therefore, we can write the equation as:
[tex]\[
0.75x - 4.00 = 84.50
\][/tex]
Now let's compare this equation with the provided options:
- Option A: [tex]\( 0.75x - 4.00 = 84.50 \)[/tex]
- Option B: [tex]\( \frac{x - 4}{84.5} = \frac{3}{4} \)[/tex]
- Option C: [tex]\( 84.50 \times 1.25 + 4.00 = x \)[/tex]
- Option D: [tex]\( 0.75(x - 4.00) = 84.50 \)[/tex]
- Option E: [tex]\( 0.25(84.50) = x - 88.50 \)[/tex]
Among these options, the equation that matches is:
А) [tex]\( 0.75x - 4.00 = 84.50 \)[/tex]
