Certainly! Let’s tackle this problem step by step:
1. Understanding the Problem Statement:
The given fraction is [tex]\( \frac{564950^}{356000} \)[/tex], where [tex]\( 564950^ \)[/tex] represents an amount that includes a discount of R109,350 at a 10% discount rate.
2. Calculate the Original Value Before Discount:
To find the original value before the discount was applied, we need to determine how much the R109,350 represents when it is 10% of the total. The formula for this is:
[tex]\[
\text{Original Value} = \frac{\text{Discount Given}}{\text{Discount Rate}} = \frac{109350}{0.10} = 1093500.0
\][/tex]
Therefore, the original value before the discount is R1,093,500.
3. Calculate the Amount Excluding the Discount:
To find the numerator of our fraction excluding the discounted amount, we subtract the discount given from the total amount:
[tex]\[
\text{Numerator Excluding Discount} = 564950 - 109350 = 455600
\][/tex]
So, the value of [tex]\( \text{Numerator Excluding Discount} \)[/tex] is R455,600.
4. Calculate the Fraction:
Now, we can compute the fraction using the numerator we just found (excluding the discount) and the given denominator:
[tex]\[
\text{Fraction} = \frac{455600}{356000}
\][/tex]
This simplifies to approximately 1.2797752808988765.
Summarizing everything:
- The total amount including discount is R564,950.
- The original value before discount was R1,093,500.
- The numerator excluding the discount amount is R455,600.
- The fraction [tex]\(\frac{455600}{356000}\)[/tex] simplifies to approximately 1.2797752808988765.
These are the detailed steps and final results for the problem!
