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Sagot :
To solve this problem, let's break it down into a detailed step-by-step solution:
### Step 1: Calculate the Total Price for Each Item
- Teak Trays:
- Number of trays: [tex]\( 90 \)[/tex]
- Price per tray: [tex]\( \$35.30 \)[/tex]
- Total price for trays: [tex]\( 90 \times 35.30 = 3176.9999999999995 \)[/tex] (approximately [tex]\( \$3177.00 \)[/tex])
- Teak Buckets:
- Number of buckets: [tex]\( 25 \)[/tex]
- Price per bucket: [tex]\( \$60.20 \)[/tex]
- Total price for buckets: [tex]\( 25 \times 60.20 = 1505.00 \)[/tex]
- Teak Salad Bowls:
- Number of bowls: [tex]\( 35 \)[/tex]
- Price per bowl: [tex]\( \$54.30 \)[/tex]
- Total price for bowls: [tex]\( 35 \times 54.30 = 1900.5 \)[/tex]
### Step 2: Calculate the Total Invoice Amount Before Discounts
- Add the total prices of all items:
- Total for trays: [tex]\( \$3177.00 \)[/tex]
- Total for buckets: [tex]\( \$1505.00 \)[/tex]
- Total for bowls: [tex]\( \$1900.50 \)[/tex]
- Total before discounts: [tex]\( 3177.00 + 1505.00 + 1900.50 = 6582.50 \)[/tex]
### Step 3: Apply Trade Discounts in Sequence
First Trade Discount of [tex]\( 34 \frac{2}{3} \% \)[/tex]
- Convert [tex]\( 34 \frac{2}{3}\% \)[/tex] to a decimal: [tex]\( 34 + \frac{2}{3}\% = 34.6667 \% \)[/tex]
- Calculate the amount after the first discount:
- [tex]\( 6582.50 \times (1 - \frac{34.6667}{100}) = 4300.566666666667 \)[/tex] (approximately [tex]\( \$4300.57 \)[/tex])
Second Trade Discount of [tex]\( 6 \frac{1}{2}\% \)[/tex]
- Convert [tex]\( 6 \frac{1}{2}\% \)[/tex] to a decimal: [tex]\( 6 + \frac{1}{2}\% = 6.5 \% \)[/tex]
- Calculate the amount after the second discount:
- [tex]\( 4300.57 \times (1 - \frac{6.5}{100}) = 4021.0298333333335 \)[/tex] (approximately [tex]\( \$4021.03 \)[/tex])
Third Trade Discount of [tex]\( 6\% \)[/tex]
- Convert [tex]\( 6\% \)[/tex] to a decimal: [tex]\( 6\% = 6 \% \)[/tex]
- Calculate the amount after the third discount:
- [tex]\( 4021.03 \times (1 - \frac{6}{100}) = 3779.7680433333335 \)[/tex] (approximately [tex]\( \$3779.77 \)[/tex])
### Step 4: Determine the Last Day of the Discount Period
- The shipment was received on June 26.
- Terms are [tex]\( 5/20 \)[/tex] R.O.G. (Receipt of Goods), meaning the discount period is 20 days from the receipt of goods.
- Calculate the last day to take the discount:
- June 26 + 20 days = July 16, 2023
### Final Answer:
The last day of the discount period is July 16, 2023.
### Step 1: Calculate the Total Price for Each Item
- Teak Trays:
- Number of trays: [tex]\( 90 \)[/tex]
- Price per tray: [tex]\( \$35.30 \)[/tex]
- Total price for trays: [tex]\( 90 \times 35.30 = 3176.9999999999995 \)[/tex] (approximately [tex]\( \$3177.00 \)[/tex])
- Teak Buckets:
- Number of buckets: [tex]\( 25 \)[/tex]
- Price per bucket: [tex]\( \$60.20 \)[/tex]
- Total price for buckets: [tex]\( 25 \times 60.20 = 1505.00 \)[/tex]
- Teak Salad Bowls:
- Number of bowls: [tex]\( 35 \)[/tex]
- Price per bowl: [tex]\( \$54.30 \)[/tex]
- Total price for bowls: [tex]\( 35 \times 54.30 = 1900.5 \)[/tex]
### Step 2: Calculate the Total Invoice Amount Before Discounts
- Add the total prices of all items:
- Total for trays: [tex]\( \$3177.00 \)[/tex]
- Total for buckets: [tex]\( \$1505.00 \)[/tex]
- Total for bowls: [tex]\( \$1900.50 \)[/tex]
- Total before discounts: [tex]\( 3177.00 + 1505.00 + 1900.50 = 6582.50 \)[/tex]
### Step 3: Apply Trade Discounts in Sequence
First Trade Discount of [tex]\( 34 \frac{2}{3} \% \)[/tex]
- Convert [tex]\( 34 \frac{2}{3}\% \)[/tex] to a decimal: [tex]\( 34 + \frac{2}{3}\% = 34.6667 \% \)[/tex]
- Calculate the amount after the first discount:
- [tex]\( 6582.50 \times (1 - \frac{34.6667}{100}) = 4300.566666666667 \)[/tex] (approximately [tex]\( \$4300.57 \)[/tex])
Second Trade Discount of [tex]\( 6 \frac{1}{2}\% \)[/tex]
- Convert [tex]\( 6 \frac{1}{2}\% \)[/tex] to a decimal: [tex]\( 6 + \frac{1}{2}\% = 6.5 \% \)[/tex]
- Calculate the amount after the second discount:
- [tex]\( 4300.57 \times (1 - \frac{6.5}{100}) = 4021.0298333333335 \)[/tex] (approximately [tex]\( \$4021.03 \)[/tex])
Third Trade Discount of [tex]\( 6\% \)[/tex]
- Convert [tex]\( 6\% \)[/tex] to a decimal: [tex]\( 6\% = 6 \% \)[/tex]
- Calculate the amount after the third discount:
- [tex]\( 4021.03 \times (1 - \frac{6}{100}) = 3779.7680433333335 \)[/tex] (approximately [tex]\( \$3779.77 \)[/tex])
### Step 4: Determine the Last Day of the Discount Period
- The shipment was received on June 26.
- Terms are [tex]\( 5/20 \)[/tex] R.O.G. (Receipt of Goods), meaning the discount period is 20 days from the receipt of goods.
- Calculate the last day to take the discount:
- June 26 + 20 days = July 16, 2023
### Final Answer:
The last day of the discount period is July 16, 2023.
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