Sure, let's break down the problem step by step to determine the value of [tex]\( m \)[/tex], the number of apps Tobias downloads.
1. Identify the cost per app without tax:
The cost of each app before tax is [tex]\( \$2.00 \)[/tex].
2. Determine the tax rate:
The tax rate is [tex]\( 10\% \)[/tex], which can also be written as [tex]\( 0.10 \)[/tex].
3. Calculate the cost per app including tax:
The tax for each app is calculated as [tex]\( 2.00 \times 0.10 = 0.20 \)[/tex].
Therefore, the total cost per app including tax is:
[tex]\[
2.00 + 0.20 = 2.20
\][/tex]
4. Total amount Tobias spends:
Tobias spends a total of [tex]\( \$52.80 \)[/tex].
5. Determine the number of apps ( [tex]\( m \)[/tex] ) Tobias can buy:
To find the number of apps, we divide the total amount spent by the total cost per app (including tax):
[tex]\[
m = \frac{52.80}{2.20}
\][/tex]
Using the given answer:
[tex]\[
m = 23.999999999999996
\][/tex]
Since [tex]\( m \)[/tex] must be an integer (as Tobias cannot download a fraction of an app), we round [tex]\( 23.999999999999996 \)[/tex] to [tex]\( 24 \)[/tex].
Thus, the value of [tex]\( m \)[/tex] is:
[tex]\[
\boxed{24}
\][/tex]
