Barbara delivered newspapers to each house on her side of the street. The house numbers on her side of the street begin with the number 705 and each increase by 6. The last house number was the largest possible number not over 799. How many papers did Barbara deliver each day?

Start with 705 and use multiples of 6 until you reach 799.

To find out how many papers Barbara delivered each day, we need to determine the number of houses on her side of the street.

The house numbers on her side of the street begin with 705 and increase by 6 for each subsequent house. We need to find the last house number on her side of the street, which is the largest possible number not over 799.

To find this, we can set up an inequality:

705 + (n - 1) * 6 ≤ 799

Where n represents the number of houses on Barbara's side of the street. Rearranging the inequality, we have:

(n - 1) * 6 ≤ 799 - 705

(n - 1) * 6 ≤ 94

Dividing both sides by 6:

n - 1 ≤ 94 ÷ 6

n - 1 ≤ 15.67

Since the number of houses can only be a whole number, we take the next lowest whole number:

n - 1 ≤ 15

Adding 1 to both sides:

n ≤ 16

Therefore, Barbara delivered newspapers to a maximum of 16 houses each day.