Given the following data for items sold by a store on different days:

| Days | Items A | % of items B | % of items C |
|----------|---------|--------------|--------------|
| Monday | 240 | 32\% | 20\% |
| Tuesday | 320 | 48\% | 12\% |
| Wednesday| 420 | 45\% | 20\% |
| Thursday | 360 | 56\% | 20\% |
| Friday | 340 | 22\% | 10\% |

If the total number of items B sold on Sunday is 25\% more than that sold on Thursday, and the total number of items C sold on Sunday is 300\% more than that sold on Friday, what is the total number of items B and items C sold by the store on Sunday?

Question

Given the following data for items sold by a store on different days:

| Days     | Items A | % of items B | % of items C |
|----------|---------|--------------|--------------|
| Monday   | 240     | 32\%         | 20\%         |
| Tuesday  | 320     | 48\%         | 12\%         |
| Wednesday| 420     | 45\%         | 20\%         |
| Thursday | 360     | 56\%         | 20\%         |
| Friday   | 340     | 22\%         | 10\%         |

If the total number of items B sold on Sunday is 25\% more than that sold on Thursday, and the total number of items C sold on Sunday is 300\% more than that sold on Friday, what is the total number of items B and items C sold by the store on Sunday?

Accepted Answer

**Solution:**

1. Calculate the total number of items B sold on Thursday:
   - Total items on Thursday = Items A + Items B + Items C
   - Given Items A on Thursday = 360
   - Percentage of items B on Thursday = 56\%
   - Percentage of items C on Thursday = 20\%

Since the percentages of B and C are given relative to total items sold, let total items sold on Thursday be $T_{Thu}$.

Using the percentage of items A, B, and C:
   $$
   \text{Items A} = 360 = (100\% - 56\% - 20\%) \times T_{Thu} = 24\% \times T_{Thu}
   $$

So,
   $$
   T_{Thu} = \frac{360}{0.24} = 1500
   $$

Now, items B on Thursday:
   $$
   \text{Items B}_{Thu} = 56\% \times 1500 = 0.56 \times 1500 = 840
   $$

2. Calculate items B sold on Sunday:
   - Sunday items B = 25\% more than Thursday
   $$
   \text{Items B}_{Sun} = 840 + 0.25 \times 840 = 1.25 \times 840 = 1050
   $$

3. Calculate total items C sold on Friday:
   - Items A on Friday = 340
   - Percentage of items B on Friday = 22\%
   - Percentage of items C on Friday = 10\%

Total items on Friday, $T_{Fri}$:
   $$
   340 = (100\% - 22\% - 10\%) \times T_{Fri} = 68\% \times T_{Fri}
   $$

So,
   $$
   T_{Fri} = \frac{340}{0.68} = 500
   $$

Items C on Friday:
   $$
   \text{Items C}_{Fri} = 10\% \times 500 = 50
   $$

4. Calculate items C sold on Sunday:
   - Sunday items C = 300\% more than Friday
   $$
   \text{Items C}_{Sun} = 50 + 3 \times 50 = 4 \times 50 = 200
   $$

5. Total items B and C sold on Sunday:
   $$
   1050 + 200 = 1250
   $$

**Answer:** 1250

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