Find the ratio of red balls sold by A and B together to blue balls sold by E.

The data in the table shows the average number of items (Red and Blue balls) sold by five shops and percentage of red balls sold.

Shops	Average number of items (Red and blue balls) sold	Percentage of red balls sold
A	50	25%
B	30	20%
C	25	20%
D	25	54%
E	35	51 $\frac{3}{7}$%

The correct option is 37:34.

Let's break down the problem step-by-step to find the ratio of red balls sold by shops A and B together to the blue balls sold by shop E.

Step 1: Understand the data given in the table
The table provides two pieces of information for each shop:
1. The average number of items (Red and Blue balls) sold. Since there are two types of items (Red and Blue), the total number of items sold by any shop is:
$\text{Total items}=2\times \text{Average number of items}$
2. The percentage of red balls sold out of the total items sold by that shop.

Step 2: Calculate the number of red balls sold by A and B together
For Shop A:
- The average number of items sold is 50.
- Therefore, the total number of items sold by A is:
$50\times 2=100$
- The percentage of red balls sold by A is 25%.
- Thus, the number of red balls sold by A is:
$25\%\text{of}100=0.25\times 100=25$
For Shop B:
- The average number of items sold is 30.
- Therefore, the total number of items sold by B is:
$30\times 2=60$
- The percentage of red balls sold by B is 20%.
- Thus, the number of red balls sold by B is:
$20\%\text{of}60=0.20\times 60=12$
Combined red balls sold by A and B together:
$25+12=37$

Step 3: Calculate the number of blue balls sold by E
For Shop E:
- The average number of items sold is 35.
- Therefore, the total number of items sold by E is:
$35\times 2=70$
- The percentage of red balls sold by E is:
$51\frac{3}{7}\%$
Let's convert this mixed fraction to an improper fraction:
$51\frac{3}{7}=\frac{51\times 7+3}{7}=\frac{357+3}{7}=\frac{360}{7}\%$
- Now, the percentage of blue balls sold by E is:
$100\%-51\frac{3}{7}\%=100\%-\frac{360}{7}\%=\frac{700-360}{7}\%=\frac{340}{7}\%$
- The number of blue balls sold by E is:
$\frac{340}{7}\%\text{of}70=\frac{340}{7\times 100}\times 70=\frac{340}{700}\times 70=\frac{340}{10}=34$

Step 4: Find the ratio
The ratio of red balls sold by A and B together to blue balls sold by E is:
$37:34$