Question

Nancy needs at least 100010001000 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 105\,\text{GB}105GB105, start text, G, B, end text available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs.

The cheapest memory cards she can find each hold 256\,\text{GB}256GB256, start text, G, B, end text and cost \$ 10$10 dollar sign, 10. She wants to spend as little money as possible and still get the storage she needs.
Let CCC represent the number of memory cards that Nancy buys.
1) Which inequality describes this scenario?

A. 105+10C \leq 1000105+10C≤1000105, plus, 10, C, is less than or equal to, 1000
B. 105+10C \geq 1000105+10C≥1000105, plus, 10, C, is greater than or equal to, 1000
C. 105+256C \leq 1000105+256C≤1000105, plus, 256, C, is less than or equal to, 1000
D. 105+256C \geq 1000105+256C≥1000"

Answer 1

The inequality describing the amount of additional memory Nancy needs for her vacation, considering she already has 105 GB on her phone, is 105 + 256C ≥ 100010001000. It represents the accumulated storage from the initial 105 GB plus what each 256 GB memory card contributes towards reaching or surpassing her needed storage capacity.

Step-by-step explanation:

Nancy needs significant additional storage to satisfy her requirements for vacation photography and video, specifically seeking at least 100010001000 gigabytes (GB) of storage. To address her needs, she is looking into purchasing memory cards, each with a capacity of 256 GB and a cost of $10.

The correct inequality to describe the scenario where C represents the number of memory cards Nancy buys is 105 + 256C ≥ 100010001000. This inequality accounts for the existing 105 GB on her phone and the additional memory each 256 GB card provides. Nancy's goal is to have a total storage capacity that is greater than or equal to her storage requirement for the trip, hence the use of the '≥' (greater than or equal to) sign.

To solve for the minimum number of cards Nancy would need to buy, we divide the additional amount of storage needed (100010001000 GB - 105 GB) by the storage capacity of a single memory card, namely 256 GB. This approach helps Nancy ensure she spends as little money as necessary while still acquiring the required storage space.