Question

beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c . if she replaces a box in the collection that contains 12 pieces of clothing with a box that contains 22 pieces of clothing, what is the average number of pieces of clothing per box for the new collection, in terms of c ?

Answer 1

To find the average number of pieces of clothing per box for the new collection, first calculate the total number of pieces of clothing in the current collection. Then account for the replacement box and calculate the new average.

Step-by-step explanation:

To find the average number of pieces of clothing per box for the new collection, we first need to calculate the total number of pieces of clothing in the current collection. Since the average number of pieces of clothing per box is c, the total number of pieces of clothing in the current collection is 8c.

When a box with 12 pieces of clothing is replaced with a box that contains 22 pieces of clothing, the total number of pieces of clothing in the new collection becomes (8c - 12 + 22) = (8c + 10).

The new average number of pieces of clothing per box is then (8c + 10)/8 = c + 1.2.