Question

Mr. Steiner needs to purchase 60 AA batteries. A nearby store sells a 20-pack of AA batteries for $12.49 and a 12-pack of the same batteries for $7.20.
i. Would it be less expensive for Mr. Steiner to purchase the batteries in 20-packs or 12-packs?
ii. What is the difference between the costs of one battery from each pack?

Answer 1

Answer:

i. It would be less expensive for Mr. Steiner to purchase the batteries in 12-packs.

ii. The difference between the costs of one battery from each pack is $0.02 or 2 cents.

Step-by-step explanation:

A way to respond to these questions is as follows:

To purchase 60 AA batteries, we have to:

• Buy 3 20-pack of AA batteries (since 3 * 20-pack = 60 batteries), or
• Buy 5 12-pack of AA batteries (since 5 * 12-pack = 60 batteries).

We also know that a 20-pack costs $12.49 and a 12-pack costs $7.20.

Part 1: Which package is less expensive?

Case 1: How much does it cost 3 20-pack of AA batteries?

Three packages cost: 3 * $12.49 = $37.47

Case 2: How much does it cost 5 12-pack of AA batteries?

Five packages cost: 5 * $7.20 = $36.00

Then, it is less expensive for Mr. Steiner to purchase 5 12-packs batteries (which cost $36) than 3 20-packs batteries (which cost $37.47).

Part 2: Difference between the costs of one battery from each pack

The question we need to answer here is, how much does it cost one battery from each pack?

For this, we need to divide the total costs that we obtained in Part 1 by the total of batteries to be purchased, that is, 60.

Then, for Case 1, the cost of one battery for this purchase is:

$\\ \frac{\ 37.47}{60battery} = \frac{\ 0.62}{battery}$ or 62 cents per battery.

For Case 2, the cost of one battery for this purchase is:

$\\ \frac{\ 36.00}{60battery} = \frac{\ 0.60}{battery}$ or 60 cents per battery.

So, the difference between the costs of one battery from each pack is:

62 cents per battery - 60 cents per battery = 2 cents per battery.

Then, one battery from 12-pack is less expensive that one battery from the 20-pack in 2 cents.