Respuesta :
Answer:
The new price of the professional sound system is 0.85 d dollars.
Step-by-step explanation:
If the original price was d dollars.
Then, the price of a professional sound system was reduced by 15%.
then, we solve the problem as follows:
New price=(original price)-15% of (original price)[tex]=d-\frac{15}{100}\cdot d[/tex]
=[tex]\frac{100\cdot d-15 \cdot d}{100}[/tex]=[tex]\frac{85d}{100}[/tex]
Therefore, the new price of the sound system is, [tex]\frac{85d}{100}[/tex] dollars or 0.85 d dollars.
The original price of professional sound system is [tex]\boxed{\$\ 0.85\text{d}}[/tex].
Further explanation:
Given:
The original price of sound system is [tex]d\text{ dollars}[/tex].
The price of professional sound system is reduced by [tex]15\%[/tex].
The objective is to find the new price of that professional sound system.
Percentage:
Percentage can be written in the ratio that is expressed as a fraction of [tex]100[/tex].
Now, convert [tex]15\%[/tex] into decimals as follows:
[tex]\begin{aligned}15\%&=\dfrac{15}{100}\\&=0.015\end{aligned}[/tex]
Let the original price of the sound system be [tex]100[/tex] dollars. Now, its price was decreased by [tex]15\%[/tex] .
The amount by which the price is reduced is calculated as follows:
[tex]\dfrac{15}{100}\times100=15[/tex]
This implies that the price is reduced by [tex]\$15[/tex].
Then its new price is calculated as follows:
[tex]100-15=85[/tex]
Given that the original price of the sound system was [tex]d[/tex] dollars.
Now, its price was reduced by [tex]15\%[/tex], means the price of sound system was reduced by [tex]15\%[/tex] of its original price.
The new price is calculated if the reduced price is subtracted from the original price as shown below:
[tex]\begin{aligned}d-0.15d&=d(1-0.15)\\&=0.85d\end{aligned}[/tex]
Now convert [tex]0.85d[/tex] into fractions as follows:
[tex]\boxed{0.85d=\dfrac{85d}{100}}[/tex]
Therefore, the new price of professional sound system is [tex]\boxed{\$\ 0.85\text{d}}[/tex].
Learn more:
1. A problem on numbers https://brainly.com/question/4736384
2. A problem on scientific notation of numbers https://brainly.com/question/4736384
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Percentage
Keywords: Price, professional, sound system, reduced, 15%, new, price, original price, d, dollars, percentage, decreased, decimals.
