Question

1. a students phone plan allows 10 gb of data per month. he uses at least 0.5 gb per day. write an inequality for the number of days he can use the phone without exceeding the data limit.
2. if he uses 0.8 gb per day, how many days can he use the data before reaching the limit?
3. how much data will he have left after 12 days at the rate of 0.6 gb per day?
4. a student works two jobs. job a pays $12 per hour; job b pays $15 per hour. she wants to earn at least $450 this week but can work no more than 35 hours total.

Explanation:

1.

Step1: Let the number of days be $d$.

The student uses at least $0.5$ GB per day, and the monthly data - limit is 10 GB.
The total data used in $d$ days is $0.5d$ GB. We want to find when the data used does not exceed the limit.
$0.5d\leq10$

Step1: Let the number of days be $d$.

The student uses 0.8 GB per day. The total data - limit is 10 GB.
We set up an equation based on the fact that the total data used should not exceed the limit. The total data used in $d$ days is $0.8d$ GB.
$0.8d\leq10$

Step2: Solve for $d$.

$d\leq\frac{10}{0.8}=\frac{100}{8} = 12.5$
Since the number of days must be a non - negative integer, the maximum number of days is 12.

Step1: Calculate the total data used in 12 days.

The student uses 0.6 GB per day. In 12 days, the total data used is $0.6\times12 = 7.2$ GB.

Step2: Calculate the remaining data.

The total data limit is 10 GB. So the remaining data is $10−7.2=2.8$ GB.

Answer:

$0.5d\leq10$

2.