Which of the following is the maximum weight of the items purchased ?

Question

A woman buys 8 items at the grocery store..the lightest item weighs 6 ounces ..the heaviest weighs 14 ounces ..the woman buys 4 items that weigh 10 ounces per item.. Which of the following is the maximum weight of the items purchased ?

Answer 1

We know there are 8 items total. We can order them by creating 8 spots like this: _ _ _ _ _ _ _ _

We are told the lightest item is 6oz and the heaviest is 14oz. This gives us, from lightest to heaviest:

6 _ _ _ _ _ _ 14

We are then told that 4 other items weigh 10oz each, but we have 6 slots left so where do we put these 4 items? The problem is asking for the maximum total weight. In order to maximize the weight we would want the heaviest possible items. The heaviest item is 14oz. There is nothing in the question that prevents more than 1 item from being 14oz.

Therefore, we should place the 10oz items toward the left like this: 6 10 10 10 10 _ _ 14.

Since we want to maximize the weight we should fill the last 2 spots with the highest weight allowed in the problem, 14oz. Therefore, we get: 6 10 10 10 10 14 14 14.

The maximum total weight for all 8 item is 88 ounces.