The table below shows the total number of volleyballs, bats, and footballs sold on five different days. It also provides the ratio of bats to footballs sold and the difference between the number of bats and footballs sold each day.

Note: The total number of volleyballs sold on Monday is equal to the total number of footballs sold on Friday.

| Days | Total (Volleyball + Bats + Footballs) | Bats : Footballs | Difference (Bats - Footballs) |
|----------|---------------------------------------|------------------|-------------------------------|
| Monday | 140 | 5 : 1 | 60 |
| Tuesday | 129 | 2 : 1 | 38 |
| Wednesday| 100 | 1 : 3 | 40 |
| Thursday | 140 | 3 : 2 | 20 |
| Friday | 130 | 1 : 1 | 0 |

What percentage more or less are the bats sold on Wednesday and Tuesday together compared to the footballs sold on Friday?

Question

The table below shows the total number of volleyballs, bats, and footballs sold on five different days. It also provides the ratio of bats to footballs sold and the difference between the number of bats and footballs sold each day.

Note: The total number of volleyballs sold on Monday is equal to the total number of footballs sold on Friday.

| Days     | Total (Volleyball + Bats + Footballs) | Bats : Footballs | Difference (Bats - Footballs) |
|----------|---------------------------------------|------------------|-------------------------------|
| Monday   | 140                                   | 5 : 1            | 60                            |
| Tuesday  | 129                                   | 2 : 1            | 38                            |
| Wednesday| 100                                   | 1 : 3            | 40                            |
| Thursday | 140                                   | 3 : 2            | 20                            |
| Friday   | 130                                   | 1 : 1            | 0                             |

What percentage more or less are the bats sold on Wednesday and Tuesday together compared to the footballs sold on Friday?

Accepted Answer

**Solution:**

1. First, find the number of bats and footballs sold on Tuesday.

- Total items sold on Tuesday = 129
   - Ratio of bats to footballs = 2 : 1
   - Difference between bats and footballs = 38

Let bats = 2x and footballs = x.

Difference = bats - footballs = 2x - x = x = 38

So, footballs on Tuesday = 38 and bats on Tuesday = 2 	imes 38 = 76

2. Next, find the number of bats and footballs sold on Wednesday.

- Total items sold on Wednesday = 100
   - Ratio of bats to footballs = 1 : 3
   - Difference between bats and footballs = 40

Let bats = y and footballs = 3y.

Difference = footballs - bats = 3y - y = 2y = 40 $$\Rightarrow$$ y = 20

So, bats on Wednesday = 20 and footballs on Wednesday = 60

3. Calculate bats sold on Tuesday and Wednesday together:

Bats (Tuesday + Wednesday) = 76 + 20 = 96

4. Find footballs sold on Friday.

- Total items sold on Friday = 130
   - Ratio of bats to footballs = 1 : 1
   - Difference between bats and footballs = 0

Since bats = footballs, let each be z.

Total = bats + footballs + volleyballs = z + z + volleyballs = 2z + volleyballs = 130

From the note, volleyballs sold on Monday = footballs sold on Friday.

Calculate volleyballs on Monday:

- Total on Monday = 140
   - Ratio of bats to footballs = 5 : 1
   - Difference between bats and footballs = 60

Let bats = 5a and footballs = a.

Difference = bats - footballs = 5a - a = 4a = 60 $$\Rightarrow$$ a = 15

So, footballs on Monday = 15

Volleyballs on Monday = Total - (bats + footballs) = 140 - (5 $$	imes $$15 + 15) = 140 - (75 + 15) = 140 - 90 = 50

Therefore, volleyballs on Monday = 50 = footballs on Friday.

So, footballs on Friday = 50

5. Calculate percentage difference:

Percentage more or less = $$\frac{	ext{Bats on Tuesday and Wednesday} - 	ext{Footballs on Friday}}{	ext{Footballs on Friday}} 	imes $$100

= $$\frac{96 - 50}{50} 	imes 100 = \frac{46}{50} 	imes 100 = 92\%	ext{ more}$$

**Answer:** 92\%

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