Justin has an I-tunes gift card worth $125. after he downloads his first app, the cards value is $118.01. after he downloads his second app, the cards value is $111.02. after he downloads his third app, the i-tunes gift card is worth $104.03. Justin wants to download as many apps as possible. what is the most number of apps Justin can download, using his i-tunes gift card
I have A(1)=118.01
A(2)=11.02
A(3)=104.03
each time I subtract $6.99
an=a1+(n-1)d
an=118.01+(14-1)-6.99
an=124.02
so a(14)=124.02
The most apps Justin can download is 14 apps.
Is this correct? thanks for checking my work and for any help.
You get the idea, but there is something missing.
You have
A(0)=125
A(1)=118.01
A(2)=111.02
...
A(n)=125-6.99n
So when the card is used up, A(n)=0, or
125-6.99n=0
Solve for n=125/6.99=17.88
Drop the fraction to get 17 as the maximum number of apps he can download.
thank you for your help
You're welcome!
Your approach is correct. Let me explain it in more detail:
Given that the initial value of Justin's iTunes gift card is $125, and after each app download, the value decreases by $6.99, we can set up the equation to calculate the value of the gift card after n app downloads:
A(n) = A(1) - (n-1) * $6.99
Substituting the given values:
A(1) = $118.01
A(2) = $111.02
A(3) = $104.03
We can solve for the value of n when A(n) reaches $0:
0 = 118.01 - (n-1) * 6.99
6.99(n - 1) = 118.01
n - 1 = 118.01 / 6.99
n - 1 = 16.88
n = 16.88 + 1
n = 17.88
Since n represents the number of app downloads, we take the integer part of 17.88, which is 17. Therefore, the maximum number of apps Justin can download is 17.
However, you made a mistake in your calculation. Instead of subtracting 6.99 for each app download, you mistakenly added it. So, the correct calculation would be:
A(n) = A(1) - (n-1) * $6.99
A(14) = $118.01 - (14-1) * $6.99
A(14) = $118.01 - 13 * $6.99
A(14) = $118.01 - $90.87
A(14) = $27.14
So, the correct answer is that Justin can download a maximum of 14 apps using his iTunes gift card.