Jim's Market couldn't keep Crunchy Critter Crackers in stock. Jim started with 300 boxes but everyone wanted them. The first day Jim sold 6 boxes, and on the second day he sold 14 boxes. Each day 8 more boxes were sold than the day before. So after two days, he had sold 20 boxes. If he kept selling the crackers at this rate, when would Jim run out of Crunchy Critter Crackers?
If he kept selling the crackers at this rate, when would Jim run out of Crunchy Critter Crackers?������� ____________
Bad!!! you no help me I no know what n is?
37
To determine when Jim would run out of Crunchy Critter Crackers, we need to find the total number of boxes sold each day until he runs out.
On the first day, Jim sold 6 boxes.
On the second day, Jim sold 14 boxes.
Each day after that, he sold 8 more boxes than the day before.
To find the total number of boxes sold each day, we can create a sequence:
6, 14, 14+8, 14+8+8, ...
To find the pattern in this sequence, we can observe that the difference between each term is 8.
Using the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
Let's apply this formula to find the number of boxes sold each day until he runs out:
a_1 = 6
d = 8
The sum of the first n terms of an arithmetic sequence can be calculated using the formula:
S_n = (n/2)(a_1 + a_n)
Let's find the number of terms that can be calculated before Jim runs out of Crunchy Critter Crackers:
S_n = 300 (as Jim started with 300 boxes)
300 = (n/2)(6 + a_n)
We already know that after two days, Jim has sold a total of 20 boxes:
a_1 + a_2 = 6 + 14 = 20
Using this information, we can derive the following equation:
20 = (2/2)(6 + a_2)
20 = 3 + a_2
a_2 = 20 - 3 = 17
We can now substitute the values for a_1 and a_2 into equation 300 = (n/2)(6 + a_n):
300 = (n/2)(6 + 17)
300 = (n/2)(23)
Divide both sides of the equation by 23:
300/23 = n/2
n/2 ≈ 13.04
Multiply both sides by 2:
n ≈ 26.08
Since the number of terms cannot be a fraction, we round up to the nearest whole number:
n = 27
Therefore, Jim would run out of Crunchy Critter Crackers after selling them for approximately 27 days.
n/2 (2*6 + (n-1)*8) >= 300
find n