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Answer:
Part A: 299 + 45A + 30B + 50c
Part B: 569 (or 570 if you round it up)
Step-by-step explanation:
Part A:
Because there is no variable for the number of PlayStation 4s, let's assume that there is only one. That will be 299.
If A is the number of wireless controllers and each wireless controller is worth 45 dollars each, the price for the wireless controller(s) is 45A.
If B is the number of wireless controller charging stations and each wireless controller charging station cost 30 dollars, then the price of the wireless controller charging station(s) is 30B
If C is the number of games and each game cost 50 dollars, then the price of the game(s) is 50C
Put that all together, and we get 299 + 45A + 30B + 50c.
Part B:
Let's plug the numbers into the formula.
A = 2
B = 1
C = 3
2018 is the 70th term of the progression.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.