# Problem of the Week Problem A and Solution Deciding About Data

## Problem

The Webb family is trying to decide on a new monthly internet plan. There are three choices:

• Plan A: $$\10$$ for the first $$10$$ GB of data, and each additional $$2$$ GB costs $$\5$$.

• Plan B: $$\40$$ for the first $$20$$ GB of data, and each additional $$10$$ GB costs $$\10$$.

• Plan C: $$\80$$ for unlimited GB of data.

Note that for Plan A, additional data has to be purchased in $$2$$ GB increments. Similarly, for Plan B, additional data has to be purchased in $$10$$ GB increments.

After keeping track of data used, the family decides they will use between $$25$$ GB and $$40$$ GB of data each month. Which plan should the Webb family choose? Justify your answer.

## Solution

One way to make a decision is to make a table showing how much each plan would cost for various amounts of data use.

Data Used (in GB) Total Cost (in $) for Plan A Total Cost (in$) for Plan B Total Cost (in \$) for Plan C
$$10$$ $$10$$ $$40$$ $$80$$
$$12$$ $$15$$ $$40$$ $$80$$
$$14$$ $$20$$ $$40$$ $$80$$
$$16$$ $$25$$ $$40$$ $$80$$
$$18$$ $$30$$ $$40$$ $$80$$
$$20$$ $$35$$ $$40$$ $$80$$
$$22$$ $$40$$ $$50$$ $$80$$
$$24$$ $$45$$ $$50$$ $$80$$
$$26$$ $$50$$ $$50$$ $$80$$
$$28$$ $$55$$ $$50$$ $$80$$
$$30$$ $$60$$ $$50$$ $$80$$
$$32$$ $$65$$ $$60$$ $$80$$
$$34$$ $$70$$ $$60$$ $$80$$
$$36$$ $$75$$ $$60$$ $$80$$
$$38$$ $$80$$ $$60$$ $$80$$
$$40$$ $$85$$ $$60$$ $$80$$

Notice that at $$25$$ GB, with Plan A they would need to get $$26$$ GB of data. This would cost $$\50$$. So, comparing the cost of the plans, we notice that Plan B is the lowest price from $$25$$ GB to $$40$$ GB. Therefore, the family should choose Plan B.

(Note that if the family uses less than $$25$$ GB per month, then Plan A is better. Also, if they use more than $$40$$ GB, then it looks like Plan B is better at first, but Plan C will eventually be better.)