Decreasing 3/4 times a number by 18 is equal to
increasing 1/5 times the number by 5.

460/11, rounded to 41.8

Step-by-step explanation:

Let's say that our number is x. The first part states that we decrease 3/4 of a number by 18. Therefore, we find (3/4) of x and subtract that by 18, or (3/4)x-18. That is then equal to increasing (1/5) of x by 5, or (1/5)x+5. Our equation is then (3/4)x-18=(1/5)x + 5.

Adding 18 to both sides, we get (3/4)x = (1/5)x + 23.

Multiplying both sides by 5 and 4 (or 20 as a whole) to remove the denominators, we get that 15x=4x + 460. Subtracting both sides by 4x, we get that 11x=460, and dividing both sides by 11, our answer is rounded to 41.8 (or just 460/11)

Feel free to ask further questions

The average age is 7.1 years.

This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.

To start, lets multiply the total number of children by their individual ages.

6 x 5 = 30 years
14 x 8 = 112 years

There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.